Finite Group Databasebeta

← C2×#10594262 #11900960

Subgroups — C2×#10594262 #11900960

Order 1152.

4181 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#883C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×#63983C211yesmaximal, characteristic, complemented
7C2×#63977C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×#63916C211yesmaximal, characteristic, complemented
12C2×#63910C211yesmaximal, characteristic, complemented
13C2×#63905C211yesmaximal, characteristic, complemented
14C2×#63890C211yesmaximal, characteristic, complemented
15C2×#63884C211yesmaximal, characteristic, complemented
16#10594262C2116yesmaximal, direct product factor
17C2×#5653—31nomaximal
18C2×#5589—31nomaximal
19C24×C3×D3C2211yescharacteristic, complemented
20C23×D32C2211yescharacteristic
21C23×D32C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C22×C4×C3⋊D3C2211yescharacteristic, complemented
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×D12C2211yescharacteristic
29C22×C3×D12C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic, complemented
31C2×D3×#67—28no—
32C2×D3×#67C2218yescomplemented
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#626C2211yescharacteristic, complemented
37C22×#625C2211yescharacteristic
38C22×#624C2211yescharacteristic, complemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C2×D3×D12—28no—
41C2×D3×D12C2218yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45#64093C2218yescomplemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#883C2218yescomplemented
53C3×#882C2218yescomplemented
54#63983C2218yescomplemented
55#63977C2218yescomplemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63958C2218yescomplemented
64#63922C2218yescomplemented
65#63921C2218yescomplemented
66#63916C2218yescomplemented
67#63910C2218yescomplemented
68#63905C2218yescomplemented
69#63890C2218yescomplemented
70#63884C2218yescomplemented
71C23×#67—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C23×D12—31no—
75C2×C3×#123—31no—
76C2×C3×#120—31no—
77C2×#953—31no—
78C2×#938—31no—
79C2×#938—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#937—31no—
83C2×#935—31no—
84C2×#929—31no—
85#5653—316no—
86#5589—316no—
87C2×#895—31no—
88C2×#895—31no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#886—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884—61no—
97C2×#883—31no—
98C2×#883D311yescharacteristic, complemented
99C2×#882—31no—
100C2×#882—31no—
101C2×#882D311yescharacteristic, complemented
102C2×D3×C22⋊C4—31no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—42no—
109C23×C3×D3—42no—
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2314yescomplemented
115C22×D32—24no—
116C22×D32—42no—
117C22×D32—42no—
118C22×D32—42no—
119C22×D32—42no—
120C22×D32D418yescomplemented
121C22×D32C2314yes—
122C22×D32C2314yescomplemented
123C22×C32×C4C2311yescharacteristic
124C22×C32×C4C2311yescharacteristic
125C2×#638—24no—
126C2×#638—42no—
127C2×#638C2314yescomplemented
128C2×#638C2314yescomplemented
129C22×C3⋊Dic3C2311yescharacteristic
130C22×C3⋊Dic3C2311yescharacteristic
131C2×C4⋊(C3⋊D3)—24no—
132C2×C4⋊(C3⋊D3)C2314yescomplemented
133C2×C4×C3⋊D3—42no—
134C2×C4×C3⋊D3C2314yescomplemented
135C2×C3×#67—24no—
136C2×C3×#67—42no—
137C2×C3×#67C2314yes—
138C2×C3×#67C2314yescomplemented
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C2×C3×D12—24no—
144C2×C3×D12—42no—
145C2×C3×D12C2314yes—
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3—24no—
148C2×C3×C4×D3C2314yescomplemented
149D3×#67—232no—
150C2×#626—24no—
151C2×#626—24no—
152C2×#626—24no—
153C2×#626—42no—
154C2×#626C2314yes—
155C2×#626C2314yescomplemented
156C2×#626C2314yescomplemented
157C2×#626C2314yescomplemented
158C2×#625—24no—
159C2×#625C2314yes—
160C2×#624—42no—
161C2×#624C2314yescomplemented
162C2×D3×Dic3—24no—
163C2×D3×Dic3C2314yescomplemented
164D3×D12—232no—
165C32×C22⋊C4C2314yescomplemented
166#3752C2314yescomplemented
167#3750C2314yescomplemented
168C3×#217C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×(C2×D3)⋊C4C2314yescomplemented
172C3×C4⋊Dic3C2314yescomplemented
173C3×Dic3⋊C4C2314yescomplemented
174Dic3⋊Dic3C2314yescomplemented
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178(C2×D3)⋊Dic3C2314yescomplemented
179(C2×D3)⋊Dic3C2314yescomplemented
180(C2×D3)⋊Dic3C2314yescomplemented
181C2×#534—91noSylow
182C25×C3—31no—
183C24×D3—31no—
184C24×D3—31no—
185C24×D3—31no—
186C24×D3—31no—
187C24×D3C2×D311yescharacteristic, complemented
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C23×C3×C4—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—38no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—31no—
204C22×#67—61no—
205C22×#67—61no—
206C22×#67—68no—
207C22×#67C2×D311yescharacteristic
208C22×#67C2×D311yescharacteristic, complemented
209C23×Dic3—31no—
210C2×D3×D4—38no—
211C2×D3×D4—38no—
212C2×D3×D4—68no—
213C2×D3×D4—68no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12—31no—
220C22×D12—38no—
221C22×D12—61no—
222C22×D12—68no—
223C22×D12C2×D311yescharacteristic
224C22×D12C2×D311yescharacteristic, complemented
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—31no—
228C22×C4×D3—31no—
229C22×C4×D3—31no—
230C22×C4×D3—61no—
231C22×C4×D3C2×D311yescharacteristic, complemented
232C3×#123—38no—
233C3×#120—38no—
234C2×C3×C4⋊C4—31no—
235C2×C3×C4⋊C4—31no—
236C2×C3×C22⋊C4—21no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C22⋊C4—31no—
241C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
242C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
243#953—38no—
244C2×#217—31no—
245C2×#217—31no—
246C2×#217—31no—
247C2×#217—31no—
248C2×#217—31no—
249C2×#217C2×D311yescharacteristic, complemented
250#938—38no—
251#938—38no—
252#937—38no—
253#937—38no—
254#937—38no—
255#935—38no—
256#929—38no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—61no—
267C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
268C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
269C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
270C2×C4⋊Dic3—31no—
271C2×C4⋊Dic3C2×D311yescharacteristic, complemented
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—61no—
276C2×Dic3⋊C4C2×D311yescharacteristic, complemented
277#895—38no—
278#895—38no—
279#894—38no—
280#894—38no—
281#886—38no—
282#884—38no—
283#884—38no—
284#884—38no—
285#884—38no—
286#884—68no—
287#883—38no—
288#883C2×D318yescomplemented
289#882—38no—
290#882—38no—
291#882C2×D318yescomplemented
292D3×C22⋊C4—38no—
293D3×C22⋊C4—38no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2412yes—
298C23×C32C2411yescharacteristic
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3C2×D414yes—
305C22×C3⋊D3C2412yes—
306C22×C3⋊D3C2412yes—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3—28no—
318C22×C3×D3—44no—
319C22×C3×D3—44no—
320C22×C3×D3—416no—
321C22×C3×D3C2×D414yes—
322C22×C3×D3C2×D414yes—
323C22×C3×D3C2412yes—
324C22×C3×D3C2412yes—
325C22×C3×D3C2412yes—
326C22×C3×D3C2412yes—
327C2×D32—28no—
328C2×D32—416no—
329C2×D32—44no—
330C2×D32—44no—
331C2×D32—44no—
332C2×D32—44no—
333C2×D32—416no—
334C2×D32C2×D4116yescomplemented
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4C2412yes—
338C2×C32×C4C2412yes—
339#638—28no—
340#638—44no—
341C2×C3⋊Dic3—22no—
342C2×C3⋊Dic3—22no—
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2412yes—
345C4⋊(C3⋊D3)—28no—
346C4×C3⋊D3—44no—
347C3×#67—28no—
348C3×#67—44no—
349C2×C3×Dic3—22no—
350C2×C3×Dic3—22no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—22no—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C3×D12—28no—
358C3×D12—44no—
359C3×C4×D3—28no—
360#626—28no—
361#626—28no—
362#626—28no—
363#626—44no—
364#625—28no—
365#624—44no—
366D3×Dic3—28no—
367C23×D4—91no—
368C23×D4—91no—
369#534—916no—
370C2×#123—31no—
371C2×#123—91no—
372C2×#123—91no—
373C2×#123—91no—
374C2×#121—91no—
375C2×#121—91no—
376C2×#121—91no—
377C2×#121—91no—
378C2×#120—31no—
379C2×#120—91no—
380C2×#120—91no—
381C2×#120—91no—
382C22×C22⋊C4—91no—
383C24×C3—21no—
384C24×C3—31no—
385C24×C3—31no—
386C24×C3—31no—
387C24×C3—31no—
388C24×C3—34no—
389C24×C3—64no—
390C24×C3—122no—
391C24×C3—122no—
392C24×C3C22×D311yescharacteristic
393C24×C3C22×D311yescharacteristic
394C23×D3—24no—
395C23×D3—31no—
396C23×D3—31no—
397C23×D3—38no—
398C23×D3—38no—
399C23×D3—34no—
400C23×D3—34no—
401C23×D3—31no—
402C23×D3—31no—
403C23×D3—34no—
404C23×D3—34no—
405C23×D3—42no—
406C23×D3—42no—
407C23×D3—61no—
408C23×D3—61no—
409C23×D3—64no—
410C23×D3—64no—
411C23×D3—122no—
412C23×D3—122no—
413C23×D3—122no—
414C23×D3—122no—
415C23×D3—122no—
416C23×D3—122no—
417C23×D3—122no—
418C23×D3—122no—
419C23×D3C22×D311yescharacteristic
420C23×D3C22×D311yescharacteristic
421C23×D3C22×D311yescharacteristic
422C23×D3C22×D311yescharacteristic
423C23×D3C22×D314yescomplemented
424C2×C3×D4—34no—
425C2×C3×D4—34no—
426C2×C3×D4—34no—
427C2×C3×D4—34no—
428C2×C3×D4—64no—
429C2×C3×D4—64no—
430C2×C3×D4—122no—
431C2×C3×D4—122no—
432C22×C3×C4—21no—
433C22×C3×C4—21no—
434C22×C3×C4—31no—
435C22×C3×C4—31no—
436C22×C3×C4—31no—
437C22×C3×C4—31no—
438C22×C3×C4—34no—
439C22×C3×C4—64no—
440C22×C3×C4C22×D311yescharacteristic
441C22×C3×C4C22×D311yescharacteristic
442C22×C3×C4C22×D311yescharacteristic
443C22×C3×C4C22×D311yescharacteristic
444C2×#67—24no—
445C2×#67—34no—
446C2×#67—34no—
447C2×#67—34no—
448C2×#67—34no—
449C2×#67—34no—
450C2×#67—34no—
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—34no—
454C2×#67—34no—
455C2×#67—42no—
456C2×#67—64no—
457C2×#67—64no—
458C2×#67—64no—
459C2×#67—64no—
460C2×#67—64no—
461C2×#67—632no—
462C2×#67—64no—
463C2×#67—64no—
464C2×#67—64no—
465C2×#67—64no—
466C2×#67—124no—
467C2×#67—122no—
468C2×#67—122no—
469C2×#67—122no—
470C2×#67—124no—
471C2×#67C22×D314yes—
472C2×#67C22×D314yescomplemented
473C22×Dic3—31no—
474C22×Dic3—31no—
475C22×Dic3—31no—
476C22×Dic3—31no—
477C22×Dic3—34no—
478C22×Dic3—61no—
479C22×Dic3—61no—
480C22×Dic3—64no—
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483C22×Dic3C22×D311yescharacteristic
484C22×Dic3C22×D311yescharacteristic
485D3×D4—632no—
486D3×D4—632no—
487C2×D12—24no—
488C2×D12—34no—
489C2×D12—34no—
490C2×D12—34no—
491C2×D12—34no—
492C2×D12—34no—
493C2×D12—34no—
494C2×D12—42no—
495C2×D12—64no—
496C2×D12—632no—
497C2×D12—64no—
498C2×D12—64no—
499C2×D12—64no—
500C2×D12—64no—
501C2×D12—64no—
502C2×D12—124no—
503C2×D12—122no—
504C2×D12C22×D314yes—
505C2×D12C22×D314yescomplemented
506C2×C4×D3—24no—
507C2×C4×D3—34no—
508C2×C4×D3—34no—
509C2×C4×D3—34no—
510C2×C4×D3—34no—
511C2×C4×D3—34no—
512C2×C4×D3—64no—
513C2×C4×D3—64no—
514C2×C4×D3—122no—
515C2×C4×D3—122no—
516C2×C4×D3—122no—
517C2×C4×D3—122no—
518C2×C4×D3—124no—
519C2×C4×D3C22×D314yescomplemented
520C3×C4⋊C4—34no—
521C3×C4⋊C4—34no—
522C3×C22⋊C4—24no—
523C3×C22⋊C4—34no—
524C3×C22⋊C4—34no—
525C3×C22⋊C4—34no—
526C3×C22⋊C4—34no—
527C3×C22⋊C4C22×D314yescomplemented
528C3×C22⋊C4C22×D314yescomplemented
529#217—34no—
530#217—34no—
531#217—34no—
532#217—34no—
533#217—34no—
534#217C22×D314yescomplemented
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4—34no—
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—64no—
545(C2×D3)⋊C4C22×D314yescomplemented
546(C2×D3)⋊C4C22×D314yescomplemented
547(C2×D3)⋊C4C22×D314yescomplemented
548C4⋊Dic3—34no—
549C4⋊Dic3C22×D314yescomplemented
550Dic3⋊C4—34no—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—64no—
554Dic3⋊C4C22×D314yescomplemented
555C22×C32—22no—
556C22×C32—22no—
557C22×C32—22no—
558C22×C32—44no—
559C22×C32C22×D412yes—
560C22×C32H(5,𝔽2)12yes—
561C22×C32H(5,𝔽2)12yes—
562C22×C32C2511yescharacteristic
563C2×C3⋊D3—28no—
564C2×C3⋊D3—22no—
565C2×C3⋊D3—22no—
566C2×C3⋊D3—22no—
567C2×C3⋊D3—22no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—44no—
570C2×C3⋊D3C22×D414yes—
571C2×C3×D3—28no—
572C2×C3×D3—28no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—22no—
576C2×C3×D3—22no—
577C2×C3×D3—22no—
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3—416no—
584C2×C3×D3—44no—
585C2×C3×D3—44no—
586C2×C3×D3C22×D414yes—
587C2×C3×D3C22×D414yes—
588D32—416no—
589D32—416no—
590C32×C4—22no—
591C32×C4—22no—
592C3⋊Dic3—22no—
593C3⋊Dic3—22no—
594C3×Dic3—22no—
595C3×Dic3—22no—
596C3×Dic3—22no—
597C3×Dic3—22no—
598C25—31no—
599C25—91no—
600C25—91no—
601C22×D4—31no—
602C22×D4—31no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4—98no—
606C22×D4—91no—
607C22×D4—91no—
608C22×D4—91no—
609C22×D4—91no—
610C22×D4—98no—
611C22×D4—91no—
612C22×D4—91no—
613C22×D4—91no—
614C22×D4—91no—
615C22×D4—188no—
616C22×D4—188no—
617C23×C4—31no—
618C23×C4—91no—
619C23×C4—91no—
620C23×C4—91no—
621#123—38no—
622#123—98no—
623#123—98no—
624#123—98no—
625#121—98no—
626#121—98no—
627#121—98no—
628#121—98no—
629#120—38no—
630#120—98no—
631#120—98no—
632#120—98no—
633C2×C4⋊C4—31no—
634C2×C4⋊C4—31no—
635C2×C4⋊C4—91no—
636C2×C4⋊C4—91no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—98no—
642C2×C22⋊C4—91no—
643C2×C22⋊C4—91no—
644C2×C22⋊C4—91no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C2×C22⋊C4—91no—
649C2×C22⋊C4D3211yescharacteristic, complemented
650C23×C3—22no—
651C23×C3—22no—
652C23×C3—22no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—22no—
656C23×C3—22no—
657C23×C3—21no—
658C23×C3—34no—
659C23×C3—34no—
660C23×C3—32no—
661C23×C3—32no—
662C23×C3—32no—
663C23×C3—32no—
664C23×C3—42no—
665C23×C3—42no—
666C23×C3—42no—
667C23×C3—68no—
668C23×C3—62no—
669C23×C3—62no—
670C23×C3—62no—
671C23×C3—62no—
672C23×C3—62no—
673C23×C3—62no—
674C23×C3—62no—
675C23×C3—62no—
676C23×C3—62no—
677C23×C3—62no—
678C23×C3—124no—
679C23×C3—124no—
680C23×C3—1216no—
681C23×C3C23×D312yes—
682C23×C3C23×D312yes—
683C23×C3C23×D311yescharacteristic
684C23×C3C23×D311yescharacteristic
685C22×D3—22no—
686C22×D3—22no—
687C22×D3—22no—
688C22×D3—22no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—22no—
695C22×D3—28no—
696C22×D3—34no—
697C22×D3—34no—
698C22×D3—32no—
699C22×D3—32no—
700C22×D3—316no—
701C22×D3—316no—
702C22×D3—32no—
703C22×D3—32no—
704C22×D3—44no—
705C22×D3—44no—
706C22×D3—416no—
707C22×D3—64no—
708C22×D3—62no—
709C22×D3—62no—
710C22×D3—68no—
711C22×D3—62no—
712C22×D3—62no—
713C22×D3—62no—
714C22×D3—62no—
715C22×D3—62no—
716C22×D3—62no—
717C22×D3—62no—
718C22×D3—62no—
719C22×D3—62no—
720C22×D3—62no—
721C22×D3—68no—
722C22×D3—122no—
723C22×D3—122no—
724C22×D3—122no—
725C22×D3—122no—
726C22×D3—122no—
727C22×D3—1216no—
728C22×D3—124no—
729C22×D3—124no—
730C22×D3—124no—
731C22×D3—124no—
732C22×D3—124no—
733C22×D3—124no—
734C22×D3—1216no—
735C22×D3—124no—
736C22×D3—124no—
737C22×D3—1216no—
738C22×D3—1216no—
739C22×D3D3×D414yes—
740C22×D3D3×D414yes—
741C22×D3C23×D312yes—
742C22×D3C23×D312yes—
743C22×D3C23×D312yes—
744C22×D3C23×D312yes—
745C3×D4—68no—
746C3×D4—68no—
747C3×D4—124no—
748C3×D4—124no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—22no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—32no—
756C2×C3×C4—32no—
757C2×C3×C4—32no—
758C2×C3×C4—32no—
759C2×C3×C4—42no—
760C2×C3×C4—42no—
761C2×C3×C4—68no—
762C2×C3×C4—62no—
763C2×C3×C4—62no—
764C2×C3×C4—62no—
765C2×C3×C4—62no—
766C2×C3×C4C23×D312yes—
767C2×C3×C4C23×D312yes—
768C2×C3×C4C23×D312yes—
769C2×C3×C4C23×D312yes—
770#67—28no—
771#67—44no—
772#67—68no—
773#67—68no—
774#67—68no—
775#67—68no—
776#67—68no—
777#67—68no—
778#67—68no—
779#67—128no—
780#67—124no—
781#67—124no—
782#67—124no—
783#67—128no—
784C2×Dic3—22no—
785C2×Dic3—22no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—32no—
789C2×Dic3—32no—
790C2×Dic3—32no—
791C2×Dic3—32no—
792C2×Dic3—62no—
793C2×Dic3—62no—
794C2×Dic3—68no—
795C2×Dic3—64no—
796C2×Dic3—62no—
797C2×Dic3—62no—
798C2×Dic3—62no—
799C2×Dic3—62no—
800C2×Dic3—122no—
801C2×Dic3C23×D312yes—
802C2×Dic3C23×D312yes—
803C2×Dic3C23×D312yes—
804C2×Dic3C23×D312yes—
805D12—28no—
806D12—44no—
807D12—68no—
808D12—68no—
809D12—68no—
810D12—68no—
811D12—68no—
812D12—128no—
813D12—124no—
814C4×D3—28no—
815C4×D3—68no—
816C4×D3—124no—
817C4×D3—124no—
818C4×D3—124no—
819C4×D3—124no—
820C4×D3—128no—
821C2×C32—42no—
822C2×C32#53414yescomplemented
823C2×C32C23×D411yescharacteristic
824C2×C32C2×H(5,𝔽2)11yescharacteristic
825C2×C32C2×H(5,𝔽2)11yescharacteristic
826C3⋊D3—24no—
827C3⋊D3—42no—
828C3×D3—24no—
829C3×D3—24no—
830C3×D3—42no—
831C3×D3—42no—
832C24—31no—
833C24—31no—
834C24—31no—
835C24—31no—
836C24—34no—
837C24—64no—
838C24—94no—
839C24—98no—
840C24—94no—
841C24—91no—
842C24—91no—
843C24—122no—
844C24—122no—
845C24—184no—
846C24—362no—
847C24—362no—
848C24—362no—
849C24—362no—
850C24C2×D3211yescharacteristic
851C2×D4—34no—
852C2×D4—34no—
853C2×D4—34no—
854C2×D4—34no—
855C2×D4—64no—
856C2×D4—64no—
857C2×D4—94no—
858C2×D4—94no—
859C2×D4—94no—
860C2×D4—94no—
861C2×D4—94no—
862C2×D4—94no—
863C2×D4—94no—
864C2×D4—94no—
865C2×D4—122no—
866C2×D4—122no—
867C2×D4—184no—
868C2×D4—1832no—
869C2×D4—184no—
870C2×D4—184no—
871C2×D4—184no—
872C2×D4—1832no—
873C2×D4—184no—
874C2×D4—184no—
875C2×D4—362no—
876C2×D4—362no—
877C22×C4—31no—
878C22×C4—31no—
879C22×C4—31no—
880C22×C4—31no—
881C22×C4—34no—
882C22×C4—64no—
883C22×C4—94no—
884C22×C4—94no—
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—94no—
888C22×C4—184no—
889C22×C4—362no—
890C22×C4—362no—
891C22×C4C2×D3211yescharacteristic
892C22×C4C2×D3211yescharacteristic
893C4⋊C4—34no—
894C4⋊C4—34no—
895C4⋊C4—94no—
896C4⋊C4—94no—
897C22⋊C4—34no—
898C22⋊C4—34no—
899C22⋊C4—34no—
900C22⋊C4—34no—
901C22⋊C4—94no—
902C22⋊C4—94no—
903C22⋊C4—94no—
904C22⋊C4—94no—
905C22⋊C4—94no—
906C22⋊C4—94no—
907C22⋊C4—94no—
908C22⋊C4C2×D3214yescomplemented
909C22×C3—22no—
910C22×C3—22no—
911C22×C3—22no—
912C22×C3—22no—
913C22×C3—22no—
914C22×C3—22no—
915C22×C3—22no—
916C22×C3—22no—
917C22×C3—22no—
918C22×C3—21no—
919C22×C3—34no—
920C22×C3—34no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—44no—
925C22×C3—44no—
926C22×C3—68no—
927C22×C3—62no—
928C22×C3—62no—
929C22×C3—62no—
930C22×C3—62no—
931C22×C3—68no—
932C22×C3—62no—
933C22×C3—62no—
934C22×C3—62no—
935C22×C3—62no—
936C22×C3—62no—
937C22×C3—62no—
938C22×C3—84no—
939C22×C3—1216no—
940C22×C3—124no—
941C22×C3—124no—
942C22×C3C2×D3×D412yes—
943C22×C3C2×D3×D412yes—
944C22×C3#100412yes—
945C22×C3#100412yes—
946C22×C3#100912yes—
947C22×C3#100912yes—
948C22×C3C24×D311yescharacteristic
949C22×C3C24×D311yescharacteristic
950C2×D3—28no—
951C2×D3—22no—
952C2×D3—22no—
953C2×D3—22no—
954C2×D3—22no—
955C2×D3—28no—
956C2×D3—22no—
957C2×D3—22no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—22no—
961C2×D3—22no—
962C2×D3—34no—
963C2×D3—34no—
964C2×D3—416no—
965C2×D3—44no—
966C2×D3—44no—
967C2×D3—64no—
968C2×D3—68no—
969C2×D3—62no—
970C2×D3—62no—
971C2×D3—62no—
972C2×D3—62no—
973C2×D3—68no—
974C2×D3—62no—
975C2×D3—62no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—62no—
979C2×D3—62no—
980C2×D3—122no—
981C2×D3—122no—
982C2×D3—128no—
983C2×D3—122no—
984C2×D3—122no—
985C2×D3—122no—
986C2×D3—1216no—
987C2×D3—1216no—
988C2×D3—1216no—
989C2×D3—1216no—
990C2×D3—124no—
991C2×D3—124no—
992C2×D3—244no—
993C2×D3C2×D3×D414yes—
994C2×D3C2×D3×D414yes—
995C3×C4—22no—
996C3×C4—22no—
997C3×C4—22no—
998C3×C4—22no—
999C3×C4—42no—
1000C3×C4—42no—
1001C3×C4—62no—
1002C3×C4—62no—
1003C3×C4—62no—
1004C3×C4—62no—
1005Dic3—22no—
1006Dic3—22no—
1007Dic3—22no—
1008Dic3—22no—
1009Dic3—64no—
1010Dic3—62no—
1011Dic3—62no—
1012Dic3—62no—
1013Dic3—62no—
1014Dic3—122no—
1015C32C2×#53411yescharacteristic, complemented, Sylow
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—34no—
1020C23—34no—
1021C23—32no—
1022C23—32no—
1023C23—32no—
1024C23—32no—
1025C23—68no—
1026C23—62no—
1027C23—62no—
1028C23—62no—
1029C23—62no—
1030C23—62no—
1031C23—62no—
1032C23—62no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—916no—
1037C23—94no—
1038C23—92no—
1039C23—92no—
1040C23—124no—
1041C23—124no—
1042C23—1216no—
1043C23—188no—
1044C23—182no—
1045C23—182no—
1046C23—182no—
1047C23—182no—
1048C23—182no—
1049C23—364no—
1050C23—364no—
1051C23—364no—
1052C23—364no—
1053C23—3616no—
1054C23—3616no—
1055C23C22×D3212yes—
1056C23C22×D3211yescharacteristic
1057D4—68no—
1058D4—68no—
1059D4—124no—
1060D4—124no—
1061D4—188no—
1062D4—188no—
1063D4—188no—
1064D4—188no—
1065D4—188no—
1066D4—188no—
1067D4—364no—
1068D4—364no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—32no—
1072C2×C4—32no—
1073C2×C4—32no—
1074C2×C4—32no—
1075C2×C4—68no—
1076C2×C4—62no—
1077C2×C4—62no—
1078C2×C4—62no—
1079C2×C4—62no—
1080C2×C4—92no—
1081C2×C4—92no—
1082C2×C4—188no—
1083C2×C4—182no—
1084C2×C4—182no—
1085C2×C4—364no—
1086C2×C4—364no—
1087C2×C4C22×D3212yes—
1088C2×C4C22×D3212yes—
1089C2×C3—21no—
1090C2×C3—21no—
1091C2×C3—21no—
1092C2×C3—24no—
1093C2×C3—42no—
1094C2×C3—42no—
1095C2×C3—64no—
1096C2×C3—64no—
1097C2×C3—82no—
1098C2×C3—122no—
1099C2×C3—122no—
1100C2×C3#558914yescomplemented
1101C2×C3#565314yescomplemented
1102C2×C3C22×D3×D411yescharacteristic
1103C2×C3C22×D3×D411yescharacteristic
1104C2×C3C2×#100411yescharacteristic
1105C2×C3C2×#100411yescharacteristic
1106C2×C3C2×#100911yescharacteristic
1107C2×C3C2×#100911yescharacteristic
1108D3—24no—
1109D3—24no—
1110D3—42no—
1111D3—42no—
1112D3—64no—
1113D3—64no—
1114D3—124no—
1115D3—122no—
1116D3—122no—
1117D3—242no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—34no—
1122C22—34no—
1123C22—44no—
1124C22—62no—
1125C22—62no—
1126C22—62no—
1127C22—62no—
1128C22—68no—
1129C22—68no—
1130C22—62no—
1131C22—62no—
1132C22—62no—
1133C22—62no—
1134C22—62no—
1135C22—62no—
1136C22—94no—
1137C22—1216no—
1138C22—124no—
1139C22—124no—
1140C22—182no—
1141C22—182no—
1142C22—188no—
1143C22—182no—
1144C22—182no—
1145C22—182no—
1146C22—3616no—
1147C22—3616no—
1148C22—364no—
1149C22#6430712yes—
1150C22D32×D412yes—
1151C22#6431412yes—
1152C22C23×D3211yescharacteristic
1153C4—22no—
1154C4—22no—
1155C4—62no—
1156C4—62no—
1157C4—62no—
1158C4—62no—
1159C4—182no—
1160C4—182no—
1161C3—21no—
1162C3C2×#558911yescharacteristic, complemented
1163C3C2×#565311yescharacteristic, complemented
1164C2—42no—
1165C2—64no—
1166C2—64no—
1167C2—122no—
1168C2—122no—
1169C2—184no—
1170C2—362no—
1171C2#1059426214yesdirect product factor
1172C2C2×#6430711yescharacteristic
1173C2C2×D32×D411yescharacteristic
1174C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#534
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×D12C2semidirect
3. C2×#64093C2semidirect
4. C2×C3×#883C2semidirect
5. C2×C3×#882C2semidirect
6. C2×#63983C2semidirect
7. C2×#63977C2semidirect
8. C2×#63958C2semidirect
9. C2×#63922C2semidirect
10. C2×#63921C2semidirect
11. C2×#63916C2semidirect
12. C2×#63910C2semidirect
13. C2×#63905C2semidirect
14. C2×#63890C2semidirect
15. C2×#63884C2semidirect
16. #10594262C2direct (N × H)
19. C24×C3×D3C22semidirect
21. C23×D32C22semidirect
22. C22×#638C22semidirect
23. C22×#638C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C4×C3⋊D3C22semidirect
27. C22×C3×#67C22semidirect
29. C22×C3×D12C22semidirect
30. C22×C3×C4×D3C22semidirect
32. C2×D3×#67C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#626C22semidirect
38. C22×#624C22semidirect
39. C22×D3×Dic3C22semidirect
41. C2×D3×D12C22semidirect
42. C2×C32×C22⋊C4C22semidirect
43. C2×#3752C22semidirect
44. C2×#3750C22semidirect
45. #64093C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#883C22semidirect
53. C3×#882C22semidirect
54. #63983C22semidirect
55. #63977C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×#3722C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63958C22semidirect
64. #63922C22semidirect
65. #63921C22semidirect
66. #63916C22semidirect
67. #63910C22semidirect
68. #63905C22semidirect
69. #63890C22semidirect
70. #63884C22semidirect
98. C2×#883D3semidirect
101. C2×#882D3semidirect
114. C23×C3×D3C23semidirect
120. C22×D32D4semidirect
122. C22×D32C23semidirect
127. C2×#638C23semidirect
128. C2×#638C23semidirect
132. C2×C4⋊(C3⋊D3)C23semidirect
134. C2×C4×C3⋊D3C23semidirect
138. C2×C3×#67C23semidirect
146. C2×C3×D12C23semidirect
148. C2×C3×C4×D3C23semidirect
155. C2×#626C23semidirect
156. C2×#626C23semidirect
157. C2×#626C23semidirect
161. C2×#624C23semidirect
163. C2×D3×Dic3C23semidirect
165. C32×C22⋊C4C23semidirect
166. #3752C23semidirect
167. #3750C23semidirect
168. C3×#217C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×(C2×D3)⋊C4C23semidirect
172. C3×C4⋊Dic3C23semidirect
173. C3×Dic3⋊C4C23semidirect
174. Dic3⋊Dic3C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
178. (C2×D3)⋊Dic3C23semidirect
179. (C2×D3)⋊Dic3C23semidirect
180. (C2×D3)⋊Dic3C23semidirect
187. C24×D3C2×D3semidirect
208. C22×#67C2×D3semidirect
224. C22×D12C2×D3semidirect
231. C22×C4×D3C2×D3semidirect
241. C2×C3×C22⋊C4C2×D3semidirect
242. C2×C3×C22⋊C4C2×D3semidirect
249. C2×#217C2×D3semidirect
267. C2×(C2×D3)⋊C4C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
269. C2×(C2×D3)⋊C4C2×D3semidirect
271. C2×C4⋊Dic3C2×D3semidirect
276. C2×Dic3⋊C4C2×D3semidirect
288. #883C2×D3semidirect
291. #882C2×D3semidirect
334. C2×D32C2×D4semidirect
423. C23×D3C22×D3semidirect
472. C2×#67C22×D3semidirect
505. C2×D12C22×D3semidirect
519. C2×C4×D3C22×D3semidirect
527. C3×C22⋊C4C22×D3semidirect
528. C3×C22⋊C4C22×D3semidirect
534. #217C22×D3semidirect
545. (C2×D3)⋊C4C22×D3semidirect
546. (C2×D3)⋊C4C22×D3semidirect
547. (C2×D3)⋊C4C22×D3semidirect
549. C4⋊Dic3C22×D3semidirect
554. Dic3⋊C4C22×D3semidirect
649. C2×C22⋊C4D32semidirect
822. C2×C32#534semidirect
908. C22⋊C4C2×D32semidirect
1015. C32C2×#534semidirect
1100. C2×C3#5589semidirect
1101. C2×C3#5653semidirect
1162. C3C2×#5589semidirect
1163. C3C2×#5653semidirect
1171. C2#10594262direct (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
C2×#640932
C2×C3×#8832
C2×C3×#8822
C2×#639832
C2×#639772
C2×#639582
C2×#639222
C2×#639212
C2×#639162
C2×#639102
C2×#639052
C2×#638902
C2×#638842
#105942622
C2×#56533
C2×#55893