Finite Group Databasebeta

← C2×D3×#884 #11900291

Subgroups — C2×D3×#884 #11900291

Order 1152.

5269 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C22×D3×D12C211yesmaximal, characteristic, complemented
4C22×C4×D32C211yesmaximal, characteristic, complemented
5C2×#64093C211yesmaximal, characteristic, complemented
6C2×C3×#884C211yesmaximal, characteristic, complemented
7C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63958C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63912C211yesmaximal, characteristic, complemented
12C2×#63910C211yesmaximal, characteristic, complemented
13C2×#63906C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16D3×#884C2116yesmaximal, direct product factor
17C2×D3×#121—31nomaximal
18C22×#884—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×D32C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C22×C4×C3⋊D3C2211yescharacteristic, complemented
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×C4×D3C2211yescharacteristic
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C2×D3×#67—28no—
33C2×D3×#67—28no—
34C2×D3×#67C2218yescomplemented
35C2×D3×#67C2218yescomplemented
36C22×#626C2211yescharacteristic, complemented
37C22×#626C2211yescharacteristic, complemented
38C22×#626C2211yescharacteristic, complemented
39C22×#626C2211yescharacteristic, complemented
40C22×#625C2211yescharacteristic, complemented
41C22×#625C2211yescharacteristic, complemented
42C22×#624C2211yescharacteristic, complemented
43C22×D3×Dic3C2211yescharacteristic
44C22×D3×Dic3C2211yescharacteristic
45C22×D3×Dic3C2211yescharacteristic, complemented
46C2×D3×D12—28no—
47C2×D3×D12C2218yescomplemented
48C2×C4×D32—28no—
49C2×C4×D32C2218yescomplemented
50C2×C32×C22⋊C4C2211yescharacteristic, complemented
51C2×#3752C2211yescharacteristic, complemented
52C2×#3750C2211yescharacteristic, complemented
53#64093C2218yescomplemented
54C2×C3×#217C2211yescharacteristic, complemented
55C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
56C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
57C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
58C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
59C3×#884C2218yescomplemented
60C3×D3×C22⋊C4C2218yescomplemented
61#63971C2218yescomplemented
62C2×#3724C2211yescharacteristic, complemented
63C2×Dic3⋊Dic3C2211yescharacteristic, complemented
64C2×#3722C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66#63958C2218yescomplemented
67D3×(C2×D3)⋊C4C2218yescomplemented
68#63912C2218yescomplemented
69#63910C2218yescomplemented
70#63906C2218yescomplemented
71#63885C2218yescomplemented
72D3×Dic3⋊C4C2218yescomplemented
73C23×#67—31no—
74C23×#67—31no—
75C22×D3×D4—31no—
76C22×D3×D4—31no—
77C22×D3×D4—31no—
78C23×D12—31no—
79C23×C4×D3—31no—
80C23×C4×D3—31no—
81C2×C3×#121—31no—
82C22×C3×C22⋊C4—31no—
83C2×#939—31no—
84C2×#939—31no—
85C2×#938—31no—
86C2×#930—31no—
87C22×(C2×D3)⋊C4—31no—
88C22×Dic3⋊C4—31no—
89D3×#121—316no—
90C2×#895—31no—
91C2×D3×C4⋊C4—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#884—31no—
100C2×#884—31no—
101C2×#884—316no—
102C2×#884—61no—
103C2×#884D311yescharacteristic, direct product factor
104C2×D3×C22⋊C4—31no—
105C2×D3×C22⋊C4D311yescharacteristic, complemented
106C24×C32C2311yescharacteristic
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2311yescharacteristic
109C23×C3×D3—24no—
110C23×C3×D3—24no—
111C23×C3×D3—24no—
112C23×C3×D3C2314yes—
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2311yescharacteristic
117C22×D32—24no—
118C22×D32—24no—
119C22×D32—24no—
120C22×D32—24no—
121C22×D32—24no—
122C22×D32D418yescomplemented
123C22×D32C2314yes—
124C22×D32C2314yes—
125C22×C32×C4C2311yescharacteristic
126C22×C32×C4C2311yescharacteristic
127C2×#638—24no—
128C2×#638—24no—
129C2×#638C2314yescomplemented
130C2×#638C2314yescomplemented
131C22×C3⋊Dic3C2311yescharacteristic
132C22×C3⋊Dic3C2311yescharacteristic
133C2×C4⋊(C3⋊D3)—24no—
134C2×C4⋊(C3⋊D3)C2314yescomplemented
135C2×C4×C3⋊D3—24no—
136C2×C4×C3⋊D3C2314yescomplemented
137C2×C3×#67—24no—
138C2×C3×#67—24no—
139C2×C3×#67C2314yescomplemented
140C2×C3×#67C2314yescomplemented
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
145C2×C3×D12—24no—
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3—24no—
148C2×C3×C4×D3—24no—
149C2×C3×C4×D3—24no—
150C2×C3×C4×D3C2314yes—
151C2×C3×C4×D3C2314yes—
152C2×C3×C4×D3C2314yescomplemented
153D3×#67—232no—
154D3×#67—232no—
155C2×#626—24no—
156C2×#626—24no—
157C2×#626—24no—
158C2×#626—24no—
159C2×#626C2314yescomplemented
160C2×#626C2314yescomplemented
161C2×#626C2314yescomplemented
162C2×#626C2314yescomplemented
163C2×#625—24no—
164C2×#625—24no—
165C2×#625C2314yescomplemented
166C2×#625C2314yescomplemented
167C2×#624—24no—
168C2×#624C2314yescomplemented
169C2×D3×Dic3—24no—
170C2×D3×Dic3—24no—
171C2×D3×Dic3D418yescomplemented
172C2×D3×Dic3C2314yes—
173C2×D3×Dic3C2314yes—
174C2×D3×Dic3C2314yescomplemented
175D3×D12—232no—
176C4×D32—232no—
177C32×C22⋊C4C2314yescomplemented
178#3752C2314yescomplemented
179#3750C2314yescomplemented
180C3×#217C2314yescomplemented
181C3×(C2×D3)⋊C4C2314yescomplemented
182C3×(C2×D3)⋊C4C2314yescomplemented
183C3×(C2×D3)⋊C4C2314yescomplemented
184C3×Dic3⋊C4C2314yescomplemented
185#3724C2314yescomplemented
186Dic3⋊Dic3C2314yescomplemented
187#3722C2314yescomplemented
188(C2×D3)⋊Dic3C2314yescomplemented
189C22×#121—91noSylow
190C25×C3—31no—
191C24×D3—31no—
192C24×D3—31no—
193C24×D3—31no—
194C24×D3—31no—
195C24×D3C2×D311yescharacteristic
196C22×C3×D4—31no—
197C22×C3×D4—31no—
198C22×C3×D4—31no—
199C23×C3×C4—31no—
200C23×C3×C4—31no—
201C23×C3×C4—31no—
202C22×#67—31no—
203C22×#67—31no—
204C22×#67—31no—
205C22×#67—31no—
206C22×#67—31no—
207C22×#67—31no—
208C22×#67—31no—
209C22×#67—31no—
210C22×#67—38no—
211C22×#67—38no—
212C22×#67—31no—
213C22×#67—31no—
214C22×#67—31no—
215C22×#67—31no—
216C22×#67—61no—
217C22×#67—61no—
218C22×#67—68no—
219C22×#67—68no—
220C22×#67C2×D311yescharacteristic, complemented
221C22×#67C2×D311yescharacteristic, complemented
222C23×Dic3—31no—
223C23×Dic3—31no—
224C23×Dic3—31no—
225C2×D3×D4—38no—
226C2×D3×D4—38no—
227C2×D3×D4—38no—
228C2×D3×D4—68no—
229C2×D3×D4—68no—
230C2×D3×D4—68no—
231C22×D12—31no—
232C22×D12—31no—
233C22×D12—31no—
234C22×D12—31no—
235C22×D12—31no—
236C22×D12—31no—
237C22×D12—38no—
238C22×D12—61no—
239C22×D12—68no—
240C22×D12C2×D311yescharacteristic, complemented
241C22×C4×D3—31no—
242C22×C4×D3—31no—
243C22×C4×D3—31no—
244C22×C4×D3—31no—
245C22×C4×D3—31no—
246C22×C4×D3—31no—
247C22×C4×D3—31no—
248C22×C4×D3—38no—
249C22×C4×D3—38no—
250C22×C4×D3—61no—
251C22×C4×D3—68no—
252C22×C4×D3—68no—
253C22×C4×D3C2×D311yescharacteristic
254C22×C4×D3C2×D311yescharacteristic
255C22×C4×D3C2×D311yescharacteristic, complemented
256C3×#121—38no—
257C2×C3×C4⋊C4—31no—
258C2×C3×C22⋊C4—21no—
259C2×C3×C22⋊C4—31no—
260C2×C3×C22⋊C4—31no—
261C2×C3×C22⋊C4—31no—
262C2×C3×C22⋊C4—31no—
263C2×C3×C22⋊C4—38no—
264C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
265C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
266C2×#217—31no—
267C2×#217C2×D311yescharacteristic, complemented
268#939—38no—
269#939—38no—
270#938—38no—
271#930—38no—
272C2×(C2×D3)⋊C4—31no—
273C2×(C2×D3)⋊C4—31no—
274C2×(C2×D3)⋊C4—31no—
275C2×(C2×D3)⋊C4—31no—
276C2×(C2×D3)⋊C4—31no—
277C2×(C2×D3)⋊C4—38no—
278C2×(C2×D3)⋊C4—61no—
279C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
280C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
281C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
282C2×C4⋊Dic3—31no—
283C2×Dic3⋊C4—31no—
284C2×Dic3⋊C4—31no—
285C2×Dic3⋊C4—31no—
286C2×Dic3⋊C4—31no—
287C2×Dic3⋊C4—31no—
288C2×Dic3⋊C4—38no—
289C2×Dic3⋊C4—61no—
290C2×Dic3⋊C4C2×D311yescharacteristic, complemented
291#895—38no—
292D3×C4⋊C4—38no—
293#884—38no—
294#884—38no—
295#884—38no—
296#884—38no—
297#884—38no—
298#884—38no—
299#884—38no—
300#884—38no—
301#884—38no—
302#884—68no—
303#884C2×D318yesdirect product factor
304D3×C22⋊C4—38no—
305D3×C22⋊C4C2×D318yescomplemented
306C23×C32—22no—
307C23×C32—22no—
308C23×C32—22no—
309C23×C32C2412yes—
310C23×C32C2411yescharacteristic
311C22×C3⋊D3—22no—
312C22×C3⋊D3—22no—
313C22×C3⋊D3—22no—
314C22×C3⋊D3—22no—
315C22×C3⋊D3—22no—
316C22×C3⋊D3C2×D414yescomplemented
317C22×C3⋊D3C2412yes—
318C22×C3⋊D3C2412yes—
319C22×C3×D3—22no—
320C22×C3×D3—22no—
321C22×C3×D3—22no—
322C22×C3×D3—22no—
323C22×C3×D3—22no—
324C22×C3×D3—22no—
325C22×C3×D3—22no—
326C22×C3×D3—22no—
327C22×C3×D3—28no—
328C22×C3×D3—28no—
329C22×C3×D3—28no—
330C22×C3×D3—416no—
331C22×C3×D3C2×D414yes—
332C22×C3×D3C2×D414yes—
333C22×C3×D3C2×D414yescomplemented
334C22×C3×D3#4114yes—
335C22×C3×D3C2412yes—
336C22×C3×D3C2412yes—
337C22×C3×D3C2412yes—
338C22×C3×D3C2412yes—
339C2×D32—232no—
340C2×D32—28no—
341C2×D32—28no—
342C2×D32—28no—
343C2×D32—28no—
344C2×D32—28no—
345C2×D32—416no—
346C2×D32C2×D4116yescomplemented
347C2×C32×C4—22no—
348C2×C32×C4—22no—
349C2×C32×C4C2412yes—
350C2×C32×C4C2412yes—
351#638—28no—
352#638—28no—
353C2×C3⋊Dic3—22no—
354C2×C3⋊Dic3C2×D414yescomplemented
355C2×C3⋊Dic3C2412yes—
356C2×C3⋊Dic3C2412yes—
357C4⋊(C3⋊D3)—28no—
358C4×C3⋊D3—28no—
359C3×#67—28no—
360C3×#67—28no—
361C2×C3×Dic3—22no—
362C2×C3×Dic3—22no—
363C2×C3×Dic3—22no—
364C2×C3×Dic3C2×D414yescomplemented
365C2×C3×Dic3C2412yes—
366C2×C3×Dic3C2412yes—
367C2×C3×Dic3C2412yes—
368C2×C3×Dic3C2412yes—
369C3×D12—28no—
370C3×C4×D3—28no—
371C3×C4×D3—28no—
372C3×C4×D3—28no—
373#626—28no—
374#626—28no—
375#626—28no—
376#626—28no—
377#625—28no—
378#625—28no—
379#624—28no—
380D3×Dic3—28no—
381D3×Dic3—28no—
382D3×Dic3C2×D4116yescomplemented
383C23×D4—91no—
384C23×D4—91no—
385C23×D4—91no—
386C24×C4—91no—
387C2×#121—31no—
388C2×#121—91no—
389C2×#121—91no—
390C2×#121—916no—
391C2×#121—91no—
392C2×#121—91no—
393C2×#121—91no—
394C2×#121—91no—
395C2×#121—91no—
396C22×C4⋊C4—91no—
397C22×C22⋊C4—31no—
398C22×C22⋊C4—91no—
399C24×C3—21no—
400C24×C3—31no—
401C24×C3—31no—
402C24×C3—34no—
403C24×C3—31no—
404C24×C3—31no—
405C24×C3—64no—
406C24×C3—64no—
407C24×C3—64no—
408C24×C3C22×D311yescharacteristic
409C24×C3C22×D311yescharacteristic
410C23×D3—24no—
411C23×D3—24no—
412C23×D3—24no—
413C23×D3—31no—
414C23×D3—31no—
415C23×D3—38no—
416C23×D3—38no—
417C23×D3—34no—
418C23×D3—34no—
419C23×D3—31no—
420C23×D3—31no—
421C23×D3—34no—
422C23×D3—34no—
423C23×D3—61no—
424C23×D3—61no—
425C23×D3—64no—
426C23×D3—64no—
427C23×D3—64no—
428C23×D3—64no—
429C23×D3—64no—
430C23×D3—64no—
431C23×D3—64no—
432C23×D3—64no—
433C23×D3—64no—
434C23×D3—64no—
435C23×D3C22×D314yes—
436C23×D3C22×D311yescharacteristic
437C23×D3C22×D311yescharacteristic
438C23×D3C22×D311yescharacteristic
439C23×D3C22×D311yescharacteristic
440C2×C3×D4—34no—
441C2×C3×D4—34no—
442C2×C3×D4—34no—
443C2×C3×D4—64no—
444C2×C3×D4—64no—
445C2×C3×D4—64no—
446C22×C3×C4—21no—
447C22×C3×C4—21no—
448C22×C3×C4—31no—
449C22×C3×C4—31no—
450C22×C3×C4—31no—
451C22×C3×C4—31no—
452C22×C3×C4—34no—
453C22×C3×C4—34no—
454C22×C3×C4—34no—
455C22×C3×C4—64no—
456C22×C3×C4—64no—
457C22×C3×C4—64no—
458C22×C3×C4C22×D311yescharacteristic
459C22×C3×C4C22×D311yescharacteristic
460C22×C3×C4C22×D311yescharacteristic
461C22×C3×C4C22×D311yescharacteristic
462C2×#67—24no—
463C2×#67—24no—
464C2×#67—34no—
465C2×#67—34no—
466C2×#67—34no—
467C2×#67—34no—
468C2×#67—34no—
469C2×#67—34no—
470C2×#67—34no—
471C2×#67—34no—
472C2×#67—34no—
473C2×#67—34no—
474C2×#67—34no—
475C2×#67—34no—
476C2×#67—64no—
477C2×#67—64no—
478C2×#67—64no—
479C2×#67—64no—
480C2×#67—64no—
481C2×#67—632no—
482C2×#67—64no—
483C2×#67—64no—
484C2×#67—64no—
485C2×#67—64no—
486C2×#67—632no—
487C2×#67—64no—
488C2×#67—64no—
489C2×#67—64no—
490C2×#67—64no—
491C2×#67—64no—
492C2×#67—124no—
493C2×#67—124no—
494C2×#67C22×D314yescomplemented
495C2×#67C22×D314yescomplemented
496C22×Dic3—31no—
497C22×Dic3—31no—
498C22×Dic3—38no—
499C22×Dic3—34no—
500C22×Dic3—31no—
501C22×Dic3—31no—
502C22×Dic3—34no—
503C22×Dic3—34no—
504C22×Dic3—61no—
505C22×Dic3—61no—
506C22×Dic3—64no—
507C22×Dic3—64no—
508C22×Dic3C22×D311yescharacteristic
509C22×Dic3C22×D311yescharacteristic
510C22×Dic3C22×D311yescharacteristic
511C22×Dic3C22×D311yescharacteristic
512D3×D4—632no—
513D3×D4—632no—
514D3×D4—632no—
515C2×D12—24no—
516C2×D12—34no—
517C2×D12—34no—
518C2×D12—34no—
519C2×D12—34no—
520C2×D12—34no—
521C2×D12—34no—
522C2×D12—64no—
523C2×D12—632no—
524C2×D12—64no—
525C2×D12—64no—
526C2×D12—64no—
527C2×D12—64no—
528C2×D12—64no—
529C2×D12—64no—
530C2×D12—124no—
531C2×D12C22×D314yescomplemented
532C2×C4×D3—24no—
533C2×C4×D3—24no—
534C2×C4×D3—24no—
535C2×C4×D3—38no—
536C2×C4×D3—34no—
537C2×C4×D3—34no—
538C2×C4×D3—34no—
539C2×C4×D3—34no—
540C2×C4×D3—34no—
541C2×C4×D3—34no—
542C2×C4×D3—34no—
543C2×C4×D3—64no—
544C2×C4×D3—632no—
545C2×C4×D3—632no—
546C2×C4×D3—64no—
547C2×C4×D3—64no—
548C2×C4×D3—64no—
549C2×C4×D3—64no—
550C2×C4×D3—64no—
551C2×C4×D3—64no—
552C2×C4×D3—124no—
553C2×C4×D3C22×D314yes—
554C2×C4×D3C22×D314yes—
555C2×C4×D3C22×D314yescomplemented
556C3×C4⋊C4—34no—
557C3×C22⋊C4—24no—
558C3×C22⋊C4—34no—
559C3×C22⋊C4—34no—
560C3×C22⋊C4—34no—
561C3×C22⋊C4—34no—
562C3×C22⋊C4C22×D314yescomplemented
563C3×C22⋊C4C22×D314yescomplemented
564#217—34no—
565#217C22×D314yescomplemented
566(C2×D3)⋊C4—34no—
567(C2×D3)⋊C4—34no—
568(C2×D3)⋊C4—34no—
569(C2×D3)⋊C4—34no—
570(C2×D3)⋊C4—34no—
571(C2×D3)⋊C4—64no—
572(C2×D3)⋊C4C22×D314yescomplemented
573(C2×D3)⋊C4C22×D314yescomplemented
574(C2×D3)⋊C4C22×D314yescomplemented
575C4⋊Dic3—34no—
576Dic3⋊C4—34no—
577Dic3⋊C4—34no—
578Dic3⋊C4—34no—
579Dic3⋊C4—34no—
580Dic3⋊C4—34no—
581Dic3⋊C4—64no—
582Dic3⋊C4C22×D314yescomplemented
583C22×C32—22no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—44no—
587C22×C32C22×D412yes—
588C22×C32C22×D412yes—
589C22×C32C2×#4112yes—
590C22×C32C2511yescharacteristic
591C2×C3⋊D3—28no—
592C2×C3⋊D3—22no—
593C2×C3⋊D3—22no—
594C2×C3⋊D3—22no—
595C2×C3⋊D3—22no—
596C2×C3⋊D3—22no—
597C2×C3⋊D3—44no—
598C2×C3⋊D3C22×D414yescomplemented
599C2×C3×D3—28no—
600C2×C3×D3—22no—
601C2×C3×D3—22no—
602C2×C3×D3—22no—
603C2×C3×D3—22no—
604C2×C3×D3—22no—
605C2×C3×D3—22no—
606C2×C3×D3—22no—
607C2×C3×D3—22no—
608C2×C3×D3—44no—
609C2×C3×D3—44no—
610C2×C3×D3—416no—
611C2×C3×D3#121116yescomplemented
612C2×C3×D3C22×D414yes—
613C2×C3×D3C22×D414yes—
614C2×C3×D3C22×D414yescomplemented
615C2×C3×D3C2×#4114yes—
616D32—232no—
617D32—416no—
618C32×C4—22no—
619C32×C4—22no—
620C3⋊Dic3—22no—
621C3⋊Dic3C22×D414yescomplemented
622C3×Dic3—22no—
623C3×Dic3—22no—
624C3×Dic3—22no—
625C3×Dic3C22×D414yescomplemented
626C25—31no—
627C25—91no—
628C25—91no—
629C22×D4—31no—
630C22×D4—31no—
631C22×D4—31no—
632C22×D4—98no—
633C22×D4—91no—
634C22×D4—91no—
635C22×D4—91no—
636C22×D4—91no—
637C22×D4—98no—
638C22×D4—98no—
639C22×D4—91no—
640C22×D4—91no—
641C22×D4—91no—
642C22×D4—91no—
643C22×D4—91no—
644C22×D4—188no—
645C22×D4—188no—
646C22×D4—188no—
647C23×C4—31no—
648C23×C4—31no—
649C23×C4—31no—
650C23×C4—91no—
651C23×C4—98no—
652C23×C4—91no—
653C23×C4—91no—
654C23×C4—91no—
655C23×C4—91no—
656C23×C4—188no—
657#121—38no—
658#121—98no—
659#121—98no—
660#121—98no—
661#121—98no—
662#121—98no—
663#121—98no—
664#121—98no—
665C2×C4⋊C4—31no—
666C2×C4⋊C4—98no—
667C2×C4⋊C4—91no—
668C2×C4⋊C4—91no—
669C2×C4⋊C4—91no—
670C2×C22⋊C4—31no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—31no—
674C2×C22⋊C4—38no—
675C2×C22⋊C4—98no—
676C2×C22⋊C4—91no—
677C2×C22⋊C4—91no—
678C2×C22⋊C4—91no—
679C2×C22⋊C4D3211yescharacteristic, complemented
680C23×C3—22no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—21no—
688C23×C3—34no—
689C23×C3—34no—
690C23×C3—34no—
691C23×C3—32no—
692C23×C3—34no—
693C23×C3—32no—
694C23×C3—32no—
695C23×C3—32no—
696C23×C3—42no—
697C23×C3—42no—
698C23×C3—42no—
699C23×C3—68no—
700C23×C3—68no—
701C23×C3—68no—
702C23×C3—62no—
703C23×C3—62no—
704C23×C3—62no—
705C23×C3—62no—
706C23×C3—62no—
707C23×C3—62no—
708C23×C3—62no—
709C23×C3—62no—
710C23×C3—1216no—
711C23×C3C23×D312yes—
712C23×C3C23×D312yes—
713C23×C3C23×D311yescharacteristic
714C23×C3C23×D311yescharacteristic
715C22×D3—22no—
716C22×D3—22no—
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—22no—
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—28no—
724C22×D3—28no—
725C22×D3—28no—
726C22×D3—34no—
727C22×D3—34no—
728C22×D3—32no—
729C22×D3—32no—
730C22×D3—316no—
731C22×D3—316no—
732C22×D3—32no—
733C22×D3—32no—
734C22×D3—416no—
735C22×D3—64no—
736C22×D3—62no—
737C22×D3—62no—
738C22×D3—68no—
739C22×D3—68no—
740C22×D3—632no—
741C22×D3—68no—
742C22×D3—68no—
743C22×D3—68no—
744C22×D3—62no—
745C22×D3—62no—
746C22×D3—62no—
747C22×D3—62no—
748C22×D3—632no—
749C22×D3—68no—
750C22×D3—68no—
751C22×D3—62no—
752C22×D3—62no—
753C22×D3—62no—
754C22×D3—62no—
755C22×D3—62no—
756C22×D3—62no—
757C22×D3—68no—
758C22×D3—68no—
759C22×D3—68no—
760C22×D3—122no—
761C22×D3—122no—
762C22×D3—122no—
763C22×D3—122no—
764C22×D3—122no—
765C22×D3—1216no—
766C22×D3—1216no—
767C22×D3#23514yes—
768C22×D3D3×D414yes—
769C22×D3D3×D414yes—
770C22×D3D3×D414yescomplemented
771C22×D3C23×D312yes—
772C22×D3C23×D312yes—
773C22×D3C23×D312yes—
774C22×D3C23×D312yes—
775C3×D4—68no—
776C3×D4—68no—
777C3×D4—68no—
778C2×C3×C4—22no—
779C2×C3×C4—22no—
780C2×C3×C4—22no—
781C2×C3×C4—22no—
782C2×C3×C4—22no—
783C2×C3×C4—22no—
784C2×C3×C4—34no—
785C2×C3×C4—32no—
786C2×C3×C4—32no—
787C2×C3×C4—32no—
788C2×C3×C4—32no—
789C2×C3×C4—42no—
790C2×C3×C4—42no—
791C2×C3×C4—68no—
792C2×C3×C4—68no—
793C2×C3×C4—68no—
794C2×C3×C4—62no—
795C2×C3×C4—62no—
796C2×C3×C4—62no—
797C2×C3×C4C23×D312yes—
798C2×C3×C4C23×D312yes—
799C2×C3×C4C23×D312yes—
800C2×C3×C4C23×D312yes—
801#67—28no—
802#67—28no—
803#67—68no—
804#67—68no—
805#67—68no—
806#67—68no—
807#67—68no—
808#67—68no—
809#67—68no—
810#67—68no—
811#67—68no—
812#67—68no—
813#67—68no—
814#67—68no—
815#67—128no—
816#67—128no—
817C2×Dic3—22no—
818C2×Dic3—22no—
819C2×Dic3—22no—
820C2×Dic3—34no—
821C2×Dic3—34no—
822C2×Dic3—32no—
823C2×Dic3—32no—
824C2×Dic3—316no—
825C2×Dic3—32no—
826C2×Dic3—32no—
827C2×Dic3—64no—
828C2×Dic3—62no—
829C2×Dic3—62no—
830C2×Dic3—68no—
831C2×Dic3—68no—
832C2×Dic3—62no—
833C2×Dic3—62no—
834C2×Dic3—122no—
835C2×Dic3D3×D414yescomplemented
836C2×Dic3C23×D312yes—
837C2×Dic3C23×D312yes—
838C2×Dic3C23×D312yes—
839C2×Dic3C23×D312yes—
840D12—28no—
841D12—68no—
842D12—68no—
843D12—68no—
844D12—68no—
845D12—68no—
846D12—68no—
847D12—128no—
848C4×D3—28no—
849C4×D3—28no—
850C4×D3—28no—
851C4×D3—316no—
852C4×D3—68no—
853C4×D3—68no—
854C4×D3—68no—
855C4×D3—68no—
856C4×D3—68no—
857C4×D3—68no—
858C4×D3—128no—
859C2×C32—42no—
860C2×C32C2×#12114yescomplemented
861C2×C32C23×D411yescharacteristic
862C2×C32C23×D411yescharacteristic
863C2×C32C22×#4111yescharacteristic
864C3⋊D3—24no—
865C3⋊D3—42no—
866C3×D3—24no—
867C3×D3—42no—
868C3×D3—42no—
869C3×D3C2×#12118yescomplemented
870C24—31no—
871C24—31no—
872C24—34no—
873C24—31no—
874C24—31no—
875C24—64no—
876C24—64no—
877C24—64no—
878C24—94no—
879C24—98no—
880C24—94no—
881C24—91no—
882C24—91no—
883C24—184no—
884C24—184no—
885C24—184no—
886C24—184no—
887C24—184no—
888C24C2×D3211yescharacteristic
889C2×D4—34no—
890C2×D4—34no—
891C2×D4—34no—
892C2×D4—64no—
893C2×D4—64no—
894C2×D4—64no—
895C2×D4—94no—
896C2×D4—94no—
897C2×D4—94no—
898C2×D4—94no—
899C2×D4—94no—
900C2×D4—94no—
901C2×D4—94no—
902C2×D4—94no—
903C2×D4—94no—
904C2×D4—184no—
905C2×D4—184no—
906C2×D4—1832no—
907C2×D4—184no—
908C2×D4—184no—
909C2×D4—184no—
910C2×D4—1832no—
911C2×D4—184no—
912C2×D4—184no—
913C2×D4—1832no—
914C2×D4—184no—
915C2×D4—184no—
916C22×C4—31no—
917C22×C4—31no—
918C22×C4—31no—
919C22×C4—31no—
920C22×C4—34no—
921C22×C4—34no—
922C22×C4—34no—
923C22×C4—64no—
924C22×C4—64no—
925C22×C4—64no—
926C22×C4—94no—
927C22×C4—94no—
928C22×C4—98no—
929C22×C4—94no—
930C22×C4—94no—
931C22×C4—91no—
932C22×C4—91no—
933C22×C4—94no—
934C22×C4—184no—
935C22×C4—184no—
936C22×C4—1832no—
937C22×C4—184no—
938C22×C4—184no—
939C22×C4C2×D3211yescharacteristic
940C22×C4C2×D3211yescharacteristic
941C4⋊C4—34no—
942C4⋊C4—94no—
943C4⋊C4—94no—
944C4⋊C4—94no—
945C22⋊C4—34no—
946C22⋊C4—34no—
947C22⋊C4—34no—
948C22⋊C4—34no—
949C22⋊C4—94no—
950C22⋊C4—94no—
951C22⋊C4—94no—
952C22⋊C4C2×D3214yescomplemented
953C22×C3—22no—
954C22×C3—22no—
955C22×C3—22no—
956C22×C3—22no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—22no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—21no—
963C22×C3—34no—
964C22×C3—34no—
965C22×C3—34no—
966C22×C3—316no—
967C22×C3—34no—
968C22×C3—42no—
969C22×C3—42no—
970C22×C3—42no—
971C22×C3—44no—
972C22×C3—44no—
973C22×C3—62no—
974C22×C3—62no—
975C22×C3—68no—
976C22×C3—62no—
977C22×C3—62no—
978C22×C3—62no—
979C22×C3—62no—
980C22×C3—62no—
981C22×C3—62no—
982C22×C3—84no—
983C22×C3—1216no—
984C22×C3—124no—
985C22×C3—124no—
986C22×C3C2×#23512yes—
987C22×C3C2×D3×D412yes—
988C22×C3C2×D3×D412yes—
989C22×C3C2×D3×D412yes—
990C22×C3C2×D3×D412yes—
991C22×C3D3×#4112yes—
992C22×C3C24×D311yescharacteristic
993C22×C3C24×D311yescharacteristic
994C2×D3—22no—
995C2×D3—22no—
996C2×D3—28no—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—22no—
1003C2×D3—34no—
1004C2×D3—34no—
1005C2×D3—44no—
1006C2×D3—44no—
1007C2×D3—416no—
1008C2×D3—64no—
1009C2×D3—632no—
1010C2×D3—62no—
1011C2×D3—62no—
1012C2×D3—62no—
1013C2×D3—62no—
1014C2×D3—68no—
1015C2×D3—68no—
1016C2×D3—632no—
1017C2×D3—62no—
1018C2×D3—62no—
1019C2×D3—62no—
1020C2×D3—62no—
1021C2×D3—62no—
1022C2×D3—62no—
1023C2×D3—122no—
1024C2×D3—122no—
1025C2×D3—128no—
1026C2×D3—122no—
1027C2×D3—122no—
1028C2×D3—122no—
1029C2×D3—1216no—
1030C2×D3—124no—
1031C2×D3—124no—
1032C2×D3—1216no—
1033C2×D3—244no—
1034C2×D3#884116yesdirect product factor
1035C2×D3C2×#23514yes—
1036C2×D3C2×D3×D414yes—
1037C2×D3C2×D3×D414yes—
1038C2×D3C2×D3×D414yescomplemented
1039C3×C4—22no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—22no—
1043C3×C4—34no—
1044C3×C4—42no—
1045C3×C4—42no—
1046C3×C4—62no—
1047C3×C4—62no—
1048C3×C4—62no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—34no—
1053Dic3—34no—
1054Dic3—64no—
1055Dic3—62no—
1056Dic3—62no—
1057Dic3—122no—
1058Dic3C2×D3×D414yescomplemented
1059C32C22×#12111yescharacteristic, complemented, Sylow
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—34no—
1064C23—34no—
1065C23—34no—
1066C23—32no—
1067C23—34no—
1068C23—32no—
1069C23—32no—
1070C23—32no—
1071C23—68no—
1072C23—68no—
1073C23—68no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—916no—
1083C23—94no—
1084C23—92no—
1085C23—92no—
1086C23—1216no—
1087C23—188no—
1088C23—188no—
1089C23—1832no—
1090C23—188no—
1091C23—188no—
1092C23—188no—
1093C23—182no—
1094C23—182no—
1095C23—182no—
1096C23—182no—
1097C23—182no—
1098C23—3616no—
1099C23C22×D3212yes—
1100C23C22×D3211yescharacteristic
1101D4—68no—
1102D4—68no—
1103D4—68no—
1104D4—188no—
1105D4—188no—
1106D4—188no—
1107D4—188no—
1108D4—188no—
1109D4—188no—
1110D4—188no—
1111D4—188no—
1112D4—188no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—34no—
1116C2×C4—32no—
1117C2×C4—32no—
1118C2×C4—32no—
1119C2×C4—32no—
1120C2×C4—68no—
1121C2×C4—68no—
1122C2×C4—68no—
1123C2×C4—62no—
1124C2×C4—62no—
1125C2×C4—62no—
1126C2×C4—916no—
1127C2×C4—94no—
1128C2×C4—92no—
1129C2×C4—92no—
1130C2×C4—188no—
1131C2×C4—188no—
1132C2×C4—188no—
1133C2×C4—188no—
1134C2×C4—182no—
1135C2×C4C22×D3212yes—
1136C2×C4C22×D3212yes—
1137C2×C3—21no—
1138C2×C3—21no—
1139C2×C3—21no—
1140C2×C3—24no—
1141C2×C3—38no—
1142C2×C3—42no—
1143C2×C3—42no—
1144C2×C3—64no—
1145C2×C3—82no—
1146C2×C3—122no—
1147C2×C3—122no—
1148C2×C3C2×#88414yescomplemented
1149C2×C3D3×#12114yescomplemented
1150C2×C3C22×#23511yescharacteristic
1151C2×C3C22×D3×D411yescharacteristic
1152C2×C3C22×D3×D411yescharacteristic
1153C2×C3C22×D3×D411yescharacteristic
1154C2×C3C22×D3×D411yescharacteristic
1155C2×C3C2×D3×#4111yescharacteristic
1156D3—24no—
1157D3—42no—
1158D3—42no—
1159D3—64no—
1160D3—64no—
1161D3—124no—
1162D3—122no—
1163D3—122no—
1164D3—242no—
1165D3C2×#88418yesdirect product factor
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—34no—
1170C22—34no—
1171C22—34no—
1172C22—316no—
1173C22—34no—
1174C22—44no—
1175C22—62no—
1176C22—62no—
1177C22—68no—
1178C22—62no—
1179C22—62no—
1180C22—62no—
1181C22—62no—
1182C22—62no—
1183C22—62no—
1184C22—94no—
1185C22—1216no—
1186C22—124no—
1187C22—124no—
1188C22—1832no—
1189C22—182no—
1190C22—182no—
1191C22—188no—
1192C22—182no—
1193C22—182no—
1194C22—182no—
1195C22—3616no—
1196C22—364no—
1197C22D3×#23512yes—
1198C22D32×D412yes—
1199C22D32×D412yes—
1200C22C23×D3211yescharacteristic
1201C4—22no—
1202C4—22no—
1203C4—34no—
1204C4—62no—
1205C4—62no—
1206C4—62no—
1207C4—94no—
1208C4—182no—
1209C3—21no—
1210C3C22×#88411yescharacteristic, complemented
1211C3C2×D3×#12111yescharacteristic, complemented
1212C2—38no—
1213C2—42no—
1214C2—64no—
1215C2—122no—
1216C2—122no—
1217C2—184no—
1218C2—362no—
1219C2D3×#88414yesdirect product factor
1220C2C2×D3×#23511yescharacteristic
1221C2C2×D32×D411yescharacteristic
1222C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C22×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C22×D3×#67C2semidirect
3. C22×D3×D12C2semidirect
4. C22×C4×D32C2semidirect
5. C2×#64093C2semidirect
6. C2×C3×#884C2semidirect
7. C2×C3×D3×C22⋊C4C2semidirect
8. C2×#63971C2semidirect
9. C2×#63958C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63912C2semidirect
12. C2×#63910C2semidirect
13. C2×#63906C2semidirect
14. C2×#63885C2semidirect
15. C2×D3×Dic3⋊C4C2semidirect
16. D3×#884C2direct (N × H)
22. C22×#638C22semidirect
23. C22×#638C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C4×C3⋊D3C22semidirect
26. C22×C3×#67C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×D12C22semidirect
31. C22×C3×C4×D3C22semidirect
34. C2×D3×#67C22semidirect
35. C2×D3×#67C22semidirect
36. C22×#626C22semidirect
37. C22×#626C22semidirect
38. C22×#626C22semidirect
39. C22×#626C22semidirect
40. C22×#625C22semidirect
41. C22×#625C22semidirect
42. C22×#624C22semidirect
45. C22×D3×Dic3C22semidirect
47. C2×D3×D12C22semidirect
49. C2×C4×D32C22semidirect
50. C2×C32×C22⋊C4C22semidirect
51. C2×#3752C22semidirect
52. C2×#3750C22semidirect
53. #64093C22semidirect
54. C2×C3×#217C22semidirect
55. C2×C3×(C2×D3)⋊C4C22semidirect
56. C2×C3×(C2×D3)⋊C4C22semidirect
57. C2×C3×(C2×D3)⋊C4C22semidirect
58. C2×C3×Dic3⋊C4C22semidirect
59. C3×#884C22semidirect
60. C3×D3×C22⋊C4C22semidirect
61. #63971C22semidirect
62. C2×#3724C22semidirect
63. C2×Dic3⋊Dic3C22semidirect
64. C2×#3722C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. #63958C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63912C22semidirect
69. #63910C22semidirect
70. #63906C22semidirect
71. #63885C22semidirect
72. D3×Dic3⋊C4C22semidirect
103. C2×#884D3direct (N × H)
105. C2×D3×C22⋊C4D3semidirect
122. C22×D32D4semidirect
129. C2×#638C23semidirect
130. C2×#638C23semidirect
134. C2×C4⋊(C3⋊D3)C23semidirect
136. C2×C4×C3⋊D3C23semidirect
139. C2×C3×#67C23semidirect
140. C2×C3×#67C23semidirect
146. C2×C3×D12C23semidirect
152. C2×C3×C4×D3C23semidirect
159. C2×#626C23semidirect
160. C2×#626C23semidirect
161. C2×#626C23semidirect
162. C2×#626C23semidirect
165. C2×#625C23semidirect
166. C2×#625C23semidirect
168. C2×#624C23semidirect
171. C2×D3×Dic3D4semidirect
174. C2×D3×Dic3C23semidirect
177. C32×C22⋊C4C23semidirect
178. #3752C23semidirect
179. #3750C23semidirect
180. C3×#217C23semidirect
181. C3×(C2×D3)⋊C4C23semidirect
182. C3×(C2×D3)⋊C4C23semidirect
183. C3×(C2×D3)⋊C4C23semidirect
184. C3×Dic3⋊C4C23semidirect
185. #3724C23semidirect
186. Dic3⋊Dic3C23semidirect
187. #3722C23semidirect
188. (C2×D3)⋊Dic3C23semidirect
220. C22×#67C2×D3semidirect
221. C22×#67C2×D3semidirect
240. C22×D12C2×D3semidirect
255. C22×C4×D3C2×D3semidirect
264. C2×C3×C22⋊C4C2×D3semidirect
265. C2×C3×C22⋊C4C2×D3semidirect
267. C2×#217C2×D3semidirect
279. C2×(C2×D3)⋊C4C2×D3semidirect
280. C2×(C2×D3)⋊C4C2×D3semidirect
281. C2×(C2×D3)⋊C4C2×D3semidirect
290. C2×Dic3⋊C4C2×D3semidirect
303. #884C2×D3direct (N × H)
305. D3×C22⋊C4C2×D3semidirect
316. C22×C3⋊D3C2×D4semidirect
333. C22×C3×D3C2×D4semidirect
346. C2×D32C2×D4semidirect
354. C2×C3⋊Dic3C2×D4semidirect
364. C2×C3×Dic3C2×D4semidirect
382. D3×Dic3C2×D4semidirect
494. C2×#67C22×D3semidirect
495. C2×#67C22×D3semidirect
531. C2×D12C22×D3semidirect
555. C2×C4×D3C22×D3semidirect
562. C3×C22⋊C4C22×D3semidirect
563. C3×C22⋊C4C22×D3semidirect
565. #217C22×D3semidirect
572. (C2×D3)⋊C4C22×D3semidirect
573. (C2×D3)⋊C4C22×D3semidirect
574. (C2×D3)⋊C4C22×D3semidirect
582. Dic3⋊C4C22×D3semidirect
598. C2×C3⋊D3C22×D4semidirect
611. C2×C3×D3#121semidirect
614. C2×C3×D3C22×D4semidirect
621. C3⋊Dic3C22×D4semidirect
625. C3×Dic3C22×D4semidirect
679. C2×C22⋊C4D32semidirect
770. C22×D3D3×D4semidirect
835. C2×Dic3D3×D4semidirect
860. C2×C32C2×#121semidirect
869. C3×D3C2×#121semidirect
952. C22⋊C4C2×D32semidirect
1034. C2×D3#884direct (N × H)
1038. C2×D3C2×D3×D4semidirect
1058. Dic3C2×D3×D4semidirect
1059. C32C22×#121semidirect
1148. C2×C3C2×#884semidirect
1149. C2×C3D3×#121semidirect
1165. D3C2×#884direct (N × H)
1210. C3C22×#884semidirect
1211. C3C2×D3×#121semidirect
1219. C2D3×#884direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D3×#672
C22×D3×D122
C22×C4×D322
C2×#640932
C2×C3×#8842
C2×C3×D3×C22⋊C42
C2×#639712
C2×#639582
C2×D3×(C2×D3)⋊C42
C2×#639122
C2×#639102
C2×#639062
C2×#638852
C2×D3×Dic3⋊C42
D3×#8842
C2×D3×#1213
C22×#8843