Finite Group Databasebeta

← C2×#10594308 #11910200

Subgroups — C2×#10594308 #11910200

Order 1152.

2901 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#884C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63979C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C2×#63978C211yesmaximal, characteristic, complemented
8C2×#63923C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63916C211yesmaximal, characteristic, complemented
11C2×#63909C211yesmaximal, characteristic, complemented
12C2×#63905C211yesmaximal, characteristic, complemented
13C2×#63858C211yesmaximal, characteristic, complemented
14C2×#63853C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594308C2116yesmaximal, direct product factor
17C2×#5666—31nomaximal
18C2×#5620—31nomaximal
19C23×D32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C23×C3×Dic3C2211yescharacteristic, complemented
28C22×C3×D12C2211yescharacteristic
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic, complemented
34C22×#625C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic
37C2×#3750C2211yescharacteristic, complemented
38#64093C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C3×#886C2218yescomplemented
46C3×#884C2218yescomplemented
47#63983C2218yescomplemented
48#63979C2218yescomplemented
49#63978C2218yescomplemented
50#63978C2218yescomplemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63923C2218yescomplemented
62#63922C2218yescomplemented
63#63916C2218yescomplemented
64#63909C2218yescomplemented
65#63905C2218yescomplemented
66#63858C2218yescomplemented
67#63853C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#940—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#938—31no—
76C2×#937—31no—
77C2×#937—31no—
78C2×#937—31no—
79C2×#930—31no—
80C2×#930—31no—
81C2×#930—31no—
82C2×#929—31no—
83#5666—316no—
84#5620—316no—
85C2×#898—31no—
86C2×#898—31no—
87C2×#898—31no—
88C2×#895—31no—
89C2×#895—31no—
90C2×#894—31no—
91C2×#886D311yescharacteristic, complemented
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—61no—
95C2×#884D311yescharacteristic, complemented
96C2×#883—31no—
97C2×#883—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#882—31no—
101C2×#879—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×D32—42no—
109C22×D32—42no—
110C22×D32—42no—
111C22×D32C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638—42no—
115C2×#638—42no—
116C2×#638C2314yes—
117C2×#638C2314yescomplemented
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C2×C4⋊(C3⋊D3)—42no—
121C2×C4⋊(C3⋊D3)C2314yes—
122C2×C4×C3⋊D3—42no—
123C2×C4×C3⋊D3C2314yescomplemented
124C2×C3×#67—42no—
125C2×C3×#67—42no—
126C2×C3×#67—42no—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yescomplemented
130C22×C3×Dic3—42no—
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yescomplemented
137C2×C3×D12—42no—
138C2×C3×D12C2314yes—
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141C2×#626—42no—
142C2×#626—42no—
143C2×#626—42no—
144C2×#626—42no—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#626C2314yes—
148C2×#626C2314yescomplemented
149C2×#625—42no—
150C2×#625C2314yes—
151C32×C22⋊C4C2314yescomplemented
152#3752C2314yes—
153#3750C2314yescomplemented
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×C4⋊Dic3C2314yescomplemented
158C3×C4⋊Dic3C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161Dic3⋊Dic3C2314yescomplemented
162#3722C2314yes—
163#3722C2314yes—
164#3722C2314yescomplemented
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yescomplemented
169Dic32C2314yescomplemented
170C2×#560—91noSylow
171C24×D3—31no—
172C24×D3—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C23×C3×C4—31no—
178C23×C3×C4—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—61no—
190C22×#67—61no—
191C22×#67C2×D311yescharacteristic
192C22×#67C2×D311yescharacteristic
193C22×#67C2×D311yescharacteristic, complemented
194C23×Dic3C2×D311yescharacteristic, complemented
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—31no—
198C22×D12—31no—
199C22×D12—31no—
200C22×D12—31no—
201C22×D12—61no—
202C22×D12C2×D311yescharacteristic
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—61no—
206C22×C4×D3C2×D311yescharacteristic, complemented
207C3×#123—38no—
208C3×#121—38no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C22⋊C4—21no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
217C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
218C2×#217—31no—
219C2×#217—31no—
220C2×#217—31no—
221C2×#217—31no—
222#940—38no—
223#940—38no—
224#939—38no—
225#939—38no—
226#938—38no—
227#937—38no—
228#937—38no—
229#937—38no—
230#930—38no—
231#930—38no—
232#930—38no—
233#929—38no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—61no—
247C2×(C2×D3)⋊C4C2×D311yescharacteristic
248C2×(C2×D3)⋊C4C2×D311yescharacteristic
249C2×(C2×D3)⋊C4C2×D311yescharacteristic
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3C2×D311yescharacteristic, complemented
253C2×C4⋊Dic3C2×D311yescharacteristic, complemented
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—61no—
259C2×Dic3⋊C4C2×D311yescharacteristic, complemented
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262#898—38no—
263#898—38no—
264#898—38no—
265#895—38no—
266#895—38no—
267#894—38no—
268#886C2×D318yescomplemented
269#884—38no—
270#884—38no—
271#884—68no—
272#884C2×D318yescomplemented
273#883—38no—
274#883—38no—
275#882—38no—
276#882—38no—
277#882—38no—
278#879—38no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32C2412yes—
283C23×C32C2411yescharacteristic
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3C2412yes—
291C22×C3⋊D3C2412yes—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C22×C3×D3C2412yes—
304C2×D32—44no—
305C2×D32—44no—
306C2×D32—44no—
307C2×D32—416no—
308C2×C32×C4—22no—
309C2×C32×C4—22no—
310C2×C32×C4C2412yes—
311C2×C32×C4C2412yes—
312#638—44no—
313#638—44no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C4⋊(C3⋊D3)—44no—
319C4×C3⋊D3—44no—
320C3×#67—44no—
321C3×#67—44no—
322C3×#67—44no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—44no—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C3×D12—44no—
335C3×C4×D3—44no—
336#626—44no—
337#626—44no—
338#626—44no—
339#626—44no—
340#625—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—91no—
344C2×#126—91no—
345C2×#123—31no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—31no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—91no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—21no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3—31no—
361C24×C3C22×D311yescharacteristic
362C24×C3C22×D311yescharacteristic
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—31no—
366C23×D3—31no—
367C23×D3—34no—
368C23×D3—34no—
369C23×D3—61no—
370C23×D3—61no—
371C23×D3—122no—
372C23×D3—122no—
373C23×D3—122no—
374C23×D3—122no—
375C23×D3—122no—
376C23×D3—122no—
377C23×D3C22×D311yescharacteristic
378C23×D3C22×D311yescharacteristic
379C23×D3C22×D311yescharacteristic
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—122no—
385C2×C3×D4—122no—
386C2×C3×D4—122no—
387C2×C3×D4—122no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—34no—
396C22×C3×C4—34no—
397C22×C3×C4—122no—
398C22×C3×C4—122no—
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—42no—
414C2×#67—42no—
415C2×#67—42no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—122no—
419C2×#67—122no—
420C2×#67—122no—
421C2×#67—122no—
422C2×#67—122no—
423C2×#67—122no—
424C2×#67—122no—
425C2×#67—122no—
426C2×#67—122no—
427C2×#67—122no—
428C2×#67—124no—
429C2×#67—124no—
430C2×#67C22×D314yes—
431C2×#67C22×D314yes—
432C2×#67C22×D314yescomplemented
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—31no—
436C22×Dic3—31no—
437C22×Dic3—42no—
438C22×Dic3—61no—
439C22×Dic3—61no—
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442C22×Dic3C22×D311yescharacteristic
443C22×Dic3C22×D311yescharacteristic
444C22×Dic3C22×D311yescharacteristic
445C22×Dic3C22×D314yescomplemented
446C2×D12—34no—
447C2×D12—34no—
448C2×D12—34no—
449C2×D12—34no—
450C2×D12—34no—
451C2×D12—34no—
452C2×D12—42no—
453C2×D12—64no—
454C2×D12—122no—
455C2×D12—122no—
456C2×D12—124no—
457C2×D12—122no—
458C2×D12—122no—
459C2×D12—122no—
460C2×D12—122no—
461C2×D12C22×D314yes—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—42no—
465C2×C4×D3—64no—
466C2×C4×D3—122no—
467C2×C4×D3—122no—
468C2×C4×D3—124no—
469C2×C4×D3C22×D314yescomplemented
470C3×C4⋊C4—34no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—34no—
473C3×C22⋊C4—24no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4—34no—
476C3×C22⋊C4—34no—
477C3×C22⋊C4C22×D314yescomplemented
478C3×C22⋊C4C22×D314yescomplemented
479#217—34no—
480#217—34no—
481#217—34no—
482#217—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—64no—
496(C2×D3)⋊C4C22×D314yes—
497(C2×D3)⋊C4C22×D314yes—
498(C2×D3)⋊C4C22×D314yes—
499C4⋊Dic3—34no—
500C4⋊Dic3—34no—
501C4⋊Dic3C22×D314yescomplemented
502C4⋊Dic3C22×D314yescomplemented
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—64no—
508Dic3⋊C4C22×D314yescomplemented
509C4×Dic3—34no—
510C4×Dic3—34no—
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—44no—
515C22×C32H(5,𝔽2)12yes—
516C22×C32H(5,𝔽2)12yes—
517C22×C32H(5,𝔽2)12yes—
518C22×C32C2511yescharacteristic
519C2×C3⋊D3—22no—
520C2×C3⋊D3—22no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—22no—
525C2×C3⋊D3—44no—
526C2×C3⋊D3—44no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—44no—
537C2×C3×D3—44no—
538C2×C3×D3—44no—
539D32—416no—
540C32×C4—22no—
541C32×C4—22no—
542C3⋊Dic3—22no—
543C3⋊Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C25—91no—
550C22×D4—31no—
551C22×D4—31no—
552C22×D4—31no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C23×C4—31no—
563C23×C4—31no—
564C23×C4—91no—
565#127—98no—
566#126—98no—
567#126—98no—
568#123—38no—
569#123—98no—
570#123—98no—
571#121—38no—
572#121—98no—
573#121—98no—
574#121—98no—
575#121—98no—
576#121—98no—
577#120—98no—
578#120—98no—
579#120—98no—
580C2×C4⋊C4—31no—
581C2×C4⋊C4—31no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—91no—
584C2×C4⋊C4—91no—
585C2×C4⋊C4—91no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C22⋊C4—91no—
597C2×C22⋊C4D3211yescharacteristic, complemented
598C2×C42—91no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—21no—
607C23×C3—32no—
608C23×C3—32no—
609C23×C3—32no—
610C23×C3—42no—
611C23×C3—42no—
612C23×C3—42no—
613C23×C3—62no—
614C23×C3—62no—
615C23×C3—62no—
616C23×C3—62no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3—62no—
620C23×C3—62no—
621C23×C3—62no—
622C23×C3C23×D312yes—
623C23×C3C23×D312yes—
624C23×C3C23×D311yescharacteristic
625C23×C3C23×D311yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—32no—
636C22×D3—32no—
637C22×D3—32no—
638C22×D3—32no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—64no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—122no—
655C22×D3—122no—
656C22×D3—122no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—124no—
664C22×D3—124no—
665C22×D3—1216no—
666C22×D3—1216no—
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×D4—124no—
671C3×D4—124no—
672C3×D4—124no—
673C3×D4—124no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—42no—
686C2×C3×C4—42no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—124no—
693C2×C3×C4—124no—
694C2×C3×C4C23×D312yes—
695C2×C3×C4C23×D312yes—
696C2×C3×C4C23×D312yes—
697C2×C3×C4C23×D312yes—
698#67—44no—
699#67—44no—
700#67—44no—
701#67—124no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67—124no—
707#67—124no—
708#67—124no—
709#67—124no—
710#67—124no—
711#67—128no—
712#67—128no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—32no—
722C2×Dic3—44no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—64no—
726C2×Dic3—62no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—122no—
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734C2×Dic3C23×D312yes—
735C2×Dic3C23×D312yes—
736D12—44no—
737D12—124no—
738D12—124no—
739D12—128no—
740D12—124no—
741D12—124no—
742D12—124no—
743D12—124no—
744C4×D3—44no—
745C4×D3—124no—
746C4×D3—124no—
747C4×D3—128no—
748C2×C32—42no—
749C2×C32#56014yescomplemented
750C2×C32C2×H(5,𝔽2)11yescharacteristic
751C2×C32C2×H(5,𝔽2)11yescharacteristic
752C2×C32C2×H(5,𝔽2)11yescharacteristic
753C3⋊D3—42no—
754C3⋊D3—42no—
755C3×D3—42no—
756C3×D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—94no—
762C24—91no—
763C24—91no—
764C24—362no—
765C24—362no—
766C24—362no—
767C24C2×D3211yescharacteristic
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—94no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—122no—
781C2×D4—122no—
782C2×D4—122no—
783C2×D4—122no—
784C2×D4—362no—
785C2×D4—362no—
786C2×D4—362no—
787C2×D4—362no—
788C2×D4—362no—
789C2×D4—362no—
790C2×D4—362no—
791C2×D4—362no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—34no—
798C22×C4—34no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—94no—
802C22×C4—122no—
803C22×C4—122no—
804C22×C4—362no—
805C22×C4C2×D3211yescharacteristic
806C22×C4C2×D3211yescharacteristic
807C4⋊C4—34no—
808C4⋊C4—34no—
809C4⋊C4—34no—
810C4⋊C4—94no—
811C4⋊C4—94no—
812C4⋊C4—94no—
813C22⋊C4—34no—
814C22⋊C4—34no—
815C22⋊C4—34no—
816C22⋊C4—94no—
817C22⋊C4—94no—
818C22⋊C4—94no—
819C22⋊C4—94no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4C2×D3214yescomplemented
825C42—94no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—44no—
840C22×C3—44no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—84no—
851C22×C3—124no—
852C22×C3—124no—
853C22×C3—124no—
854C22×C3#100412yes—
855C22×C3#100412yes—
856C22×C3#100412yes—
857C22×C3#100912yes—
858C22×C3#100912yes—
859C22×C3#100912yes—
860C22×C3C24×D311yescharacteristic
861C22×C3C24×D311yescharacteristic
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—44no—
872C2×D3—44no—
873C2×D3—44no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—122no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—1216no—
893C2×D3—1216no—
894C2×D3—128no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—124no—
898C2×D3—124no—
899C2×D3—244no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—22no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—62no—
907C3×C4—62no—
908C3×C4—62no—
909C3×C4—62no—
910C3×C4—62no—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—22no—
915Dic3—22no—
916Dic3—64no—
917Dic3—62no—
918Dic3—62no—
919Dic3—62no—
920Dic3—62no—
921Dic3—122no—
922C32C2×#56011yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—32no—
927C23—32no—
928C23—32no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—92no—
939C23—92no—
940C23—182no—
941C23—182no—
942C23—182no—
943C23—182no—
944C23—182no—
945C23—182no—
946C23—364no—
947C23—364no—
948C23—364no—
949C23—3616no—
950C23C22×D3212yes—
951C23C22×D3211yescharacteristic
952D4—124no—
953D4—124no—
954D4—124no—
955D4—124no—
956D4—364no—
957D4—364no—
958D4—364no—
959D4—364no—
960D4—364no—
961D4—364no—
962D4—364no—
963D4—364no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—92no—
977C2×C4—92no—
978C2×C4—124no—
979C2×C4—124no—
980C2×C4—182no—
981C2×C4—182no—
982C2×C4—364no—
983C2×C4C22×D3212yes—
984C2×C4C22×D3212yes—
985C2×C3—24no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—42no—
990C2×C3—42no—
991C2×C3—82no—
992C2×C3—122no—
993C2×C3—122no—
994C2×C3—122no—
995C2×C3#562014yescomplemented
996C2×C3#566614yescomplemented
997C2×C3C2×#100411yescharacteristic
998C2×C3C2×#100411yescharacteristic
999C2×C3C2×#100411yescharacteristic
1000C2×C3C2×#100911yescharacteristic
1001C2×C3C2×#100911yescharacteristic
1002C2×C3C2×#100911yescharacteristic
1003D3—42no—
1004D3—42no—
1005D3—42no—
1006D3—124no—
1007D3—122no—
1008D3—122no—
1009D3—122no—
1010D3—122no—
1011D3—242no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—44no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—124no—
1026C22—124no—
1027C22—124no—
1028C22—182no—
1029C22—182no—
1030C22—182no—
1031C22—182no—
1032C22—182no—
1033C22—182no—
1034C22—3616no—
1035C22—364no—
1036C22—364no—
1037C22#6430712yes—
1038C22#6431412yes—
1039C22#6431412yes—
1040C22C23×D3211yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—62no—
1044C4—62no—
1045C4—62no—
1046C4—62no—
1047C4—62no—
1048C4—182no—
1049C4—182no—
1050C3—21no—
1051C3C2×#562011yescharacteristic, complemented
1052C3C2×#566611yescharacteristic, complemented
1053C2—42no—
1054C2—122no—
1055C2—122no—
1056C2—122no—
1057C2—362no—
1058C2—362no—
1059C2#1059430814yesdirect product factor
1060C2C2×#6430711yescharacteristic
1061C2C2×#6431411yescharacteristic
1062C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64093C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#884C2semidirect
4. C2×#63983C2semidirect
5. C2×#63979C2semidirect
6. C2×#63978C2semidirect
7. C2×#63978C2semidirect
8. C2×#63923C2semidirect
9. C2×#63922C2semidirect
10. C2×#63916C2semidirect
11. C2×#63909C2semidirect
12. C2×#63905C2semidirect
13. C2×#63858C2semidirect
14. C2×#63853C2semidirect
15. C2×#63848C2semidirect
16. #10594308C2direct (N × H)
21. C22×#638C22semidirect
23. C22×C4×C3⋊D3C22semidirect
26. C22×C3×#67C22semidirect
27. C23×C3×Dic3C22semidirect
29. C22×C3×C4×D3C22semidirect
33. C22×#626C22semidirect
35. C2×C32×C22⋊C4C22semidirect
37. C2×#3750C22semidirect
38. #64093C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C3×#886C22semidirect
46. C3×#884C22semidirect
47. #63983C22semidirect
48. #63979C22semidirect
49. #63978C22semidirect
50. #63978C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
55. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×Dic32C22semidirect
61. #63923C22semidirect
62. #63922C22semidirect
63. #63916C22semidirect
64. #63909C22semidirect
65. #63905C22semidirect
66. #63858C22semidirect
67. #63853C22semidirect
68. #63848C22semidirect
91. C2×#886D3semidirect
95. C2×#884D3semidirect
117. C2×#638C23semidirect
123. C2×C4×C3⋊D3C23semidirect
129. C2×C3×#67C23semidirect
136. C22×C3×Dic3C23semidirect
140. C2×C3×C4×D3C23semidirect
148. C2×#626C23semidirect
151. C32×C22⋊C4C23semidirect
153. #3750C23semidirect
157. C3×C4⋊Dic3C23semidirect
158. C3×C4⋊Dic3C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. Dic3⋊Dic3C23semidirect
161. Dic3⋊Dic3C23semidirect
164. #3722C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. Dic32C23semidirect
193. C22×#67C2×D3semidirect
194. C23×Dic3C2×D3semidirect
206. C22×C4×D3C2×D3semidirect
216. C2×C3×C22⋊C4C2×D3semidirect
217. C2×C3×C22⋊C4C2×D3semidirect
252. C2×C4⋊Dic3C2×D3semidirect
253. C2×C4⋊Dic3C2×D3semidirect
259. C2×Dic3⋊C4C2×D3semidirect
268. #886C2×D3semidirect
272. #884C2×D3semidirect
432. C2×#67C22×D3semidirect
445. C22×Dic3C22×D3semidirect
469. C2×C4×D3C22×D3semidirect
477. C3×C22⋊C4C22×D3semidirect
478. C3×C22⋊C4C22×D3semidirect
501. C4⋊Dic3C22×D3semidirect
502. C4⋊Dic3C22×D3semidirect
508. Dic3⋊C4C22×D3semidirect
597. C2×C22⋊C4D32semidirect
749. C2×C32#560semidirect
824. C22⋊C4C2×D32semidirect
922. C32C2×#560semidirect
995. C2×C3#5620semidirect
996. C2×C3#5666semidirect
1051. C3C2×#5620semidirect
1052. C3C2×#5666semidirect
1059. C2#10594308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640932
C2×C3×#8862
C2×C3×#8842
C2×#639832
C2×#639792
C2×#639782
C2×#639232
C2×#639222
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