Finite Group Databasebeta

← C3×#83429 #11878546

Subgroups — C3×#83429 #11878546

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#537C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6C3×#5052C211yesmaximal, characteristic, complemented
7C3×#5048C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5043C211yesmaximal, characteristic, complemented
10C3×#5041C211yesmaximal, characteristic, complemented
11C3×#5039C211yesmaximal, characteristic, complemented
12C3×#5037C211yesmaximal, characteristic, complemented
13C3×#5034C211yesmaximal, characteristic, complemented
14C3×#4971C211yesmaximal, characteristic, complemented
15C3×#4968C211yesmaximal, characteristic, complemented
16C3×#3204—31nomaximal
17#83429C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×C22⋊Q8—21no—
22C32×C22⋊Q8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C32×#121—21no—
25C32×#121—21no—
26C32×#121—21no—
27C32×#121C2211yescharacteristic
28C32×#121C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C3×#946—21no—
31C2×C3×#216C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C3×#939—21no—
34C3×#939—21no—
35C3×#938—21no—
36C2×C3×#214C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#930C2211yescharacteristic
39C3×#930C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C3×#924C2211yescharacteristic
42C3×#924C2211yescharacteristic
43C2×C3×#208C2211yescharacteristic
44C22×C3×C3⋊C8C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#830C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#808C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#537—21no—
62C3×#537—31no—
63C3×#537D311yescharacteristic, complemented
64C3×#537C2×C311yescharacteristic, complemented
65#5833C2×C311yescharacteristic, complemented
66C3×#483—31no—
67C3×#483—31no—
68C3×#481—31no—
69C3×#481—31no—
70C3×#470—31no—
71C3×#469—31no—
72C3×#465—31no—
73C3×#465—31no—
74C3×#452—31no—
75C3×#452—31no—
76C3×#449—31no—
77C3×#449—31no—
78C3×#408—31no—
79#5239C2×C311yescharacteristic, complemented
80#5238C2×C311yescharacteristic, complemented
81#5234C2×C311yescharacteristic, complemented
82#5052C2×C311yescharacteristic, complemented
83#5048C2×C311yescharacteristic, complemented
84#5047C2×C311yescharacteristic, complemented
85#5043C2×C311yescharacteristic, complemented
86#5041C2×C311yescharacteristic, complemented
87#5039C2×C311yescharacteristic, complemented
88#5037C2×C311yescharacteristic, complemented
89#5034C2×C311yescharacteristic, complemented
90#4971C2×C311yescharacteristic, complemented
91#4968C2×C311yescharacteristic, complemented
92C32×#41—41no—
93C32×#41—41no—
94C32×#41—41no—
95C32×#41—41no—
96C2×C32×Q8D411yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4D411yescharacteristic
102C2×C32×D4D411yescharacteristic
103C2×C32×D4D411yescharacteristic
104C2×C32×D4C2311yescharacteristic
105C22×C32×C4—21no—
106C22×C32×C4—21no—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C22×C3×Dic3—21no—
114C3×#235—41no—
115C3×#235—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×Dic6C2311yescharacteristic
119C32×C4⋊C4—21no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C32×C22⋊C4—21no—
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#216—41no—
131C3×#215—41no—
132C3×#214—41no—
133C3×#213—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×#208—41no—
142C2×C3×C3⋊C8—41no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3204—31noSylow
148C2×C3×#41—21no—
149C2×C3×#41—21no—
150C2×C3×#41—31no—
151C2×C3×#41C2×D311yescharacteristic
152C2×C3×#41C2×D311yescharacteristic
153C2×C3×#41C22×C311yescharacteristic
154C2×C3×#41C22×C311yescharacteristic
155C2×#235C22×C311yescharacteristic
156C2×C3×Q16—31no—
157C2×C3×SD16—31no—
158C2×C3×SD16—31no—
159C2×C3×D8—31no—
160C2×C3×M16—31no—
161C22×C3×C8—31no—
162C3×C22⋊Q8—22no—
163C3×C22⋊Q8—21no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—21no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×C22⋊Q8C22×C311yescharacteristic
174C3×#121—22no—
175C3×#121—22no—
176C3×#121—22no—
177C3×#121—21no—
178C3×#121—21no—
179C3×#121—21no—
180C3×#121—21no—
181C3×#121—21no—
182C3×#121—21no—
183C3×#121—21no—
184C3×#121—21no—
185C3×#121—31no—
186C3×#121—31no—
187C3×#121—61no—
188C3×#121—61no—
189C3×#121—61no—
190C3×#121C2×D311yescharacteristic
191C3×#121C2×D311yescharacteristic
192C3×#121C22×C311yescharacteristic
193C3×#121C22×C311yescharacteristic
194C2×C3×C4⋊C4—21no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4C2×D311yescharacteristic
197C2×C3×C4⋊C4C22×C311yescharacteristic
198#946—21no—
199C2×#216C22×C311yescharacteristic
200C2×#215C22×C311yescharacteristic
201#939—21no—
202#939—21no—
203#938—21no—
204C2×#214C22×C311yescharacteristic
205C2×#213C22×C311yescharacteristic
206#930C22×C311yescharacteristic
207#930C22×C311yescharacteristic
208C2×C4⋊Dic3C22×C311yescharacteristic
209#924C22×C311yescharacteristic
210#924C22×C311yescharacteristic
211C2×#208C22×C311yescharacteristic
212C22×C3⋊C8C22×C311yescharacteristic
213C3×#106—31no—
214C3×#106—31no—
215C3×#106—31no—
216C3×#106—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#103—31no—
220C3×#103—31no—
221C3×#102—31no—
222C3×#102—31no—
223C3×#102—31no—
224C3×#102—31no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8—31no—
227C3×C22⋊C8—31no—
228C3×C22⋊C8—31no—
229#835C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#832C22×C311yescharacteristic
233#830C22×C311yescharacteristic
234#830C22×C311yescharacteristic
235#830C22×C311yescharacteristic
236#830C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#810C22×C311yescharacteristic
239#809C22×C311yescharacteristic
240#809C22×C311yescharacteristic
241#808C22×C311yescharacteristic
242#808C22×C311yescharacteristic
243#808C22×C311yescharacteristic
244#808C22×C311yescharacteristic
245C23×C32—21no—
246C23×C32C2×D411yescharacteristic
247C23×C32C2×D411yescharacteristic
248C23×C32C2×D411yescharacteristic
249C22×C3×D3—21no—
250C32×Q8—21no—
251C32×Q8—21no—
252C32×Q8—41no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—41no—
256C32×D4—41no—
257C32×D4—41no—
258C32×D4—42no—
259C32×D4—81no—
260C32×D4—81no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4—81no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C3×#67—42no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—81no—
283C3×D12—21no—
284C3×D12—21no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291C3×C3⋊C8—21no—
292#537—31no—
293#537C3×D311yescharacteristic, complemented
294#483—31no—
295#483—31no—
296#481—31no—
297#481—31no—
298#470—31no—
299#469—31no—
300#465—31no—
301#465—31no—
302#452—31no—
303#452—31no—
304#449—31no—
305#449—31no—
306#408—31no—
307C3×#41—41no—
308C3×#41—41no—
309C3×#41—41no—
310C3×#41—41no—
311C3×#41—41no—
312C3×#41—41no—
313C3×#41—41no—
314C3×#41—41no—
315C3×#41—42no—
316C3×#41—42no—
317C3×#41—42no—
318C3×#41—42no—
319C3×#41—121no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8#6711yescharacteristic
325C2×C3×Q8C3×D411yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C23×C311yescharacteristic
328C2×C3×D4—22no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—31no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4#6711yescharacteristic
346C2×C3×D4#6711yescharacteristic
347C2×C3×D4#6711yescharacteristic
348C2×C3×D4C3×D411yescharacteristic
349C2×C3×D4C3×D411yescharacteristic
350C2×C3×D4C3×D411yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C23×C311yescharacteristic
353C22×C3×C4—22no—
354C22×C3×C4—22no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C23×C311yescharacteristic
368C22×C3×C4C23×C311yescharacteristic
369C22×C3×C4C23×C311yescharacteristic
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—21no—
373C22×Dic3—21no—
374#235—41no—
375#235—41no—
376C2×D12C23×C311yescharacteristic
377C2×C4×D3—21no—
378C2×Dic6C23×C311yescharacteristic
379C3×Q16—121no—
380C3×SD16—121no—
381C3×SD16—121no—
382C3×D8—121no—
383C3×M16—121no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8—31no—
388C2×C3×C8—121no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C4⋊C4C23×C311yescharacteristic
408C3×C4⋊C4C23×C311yescharacteristic
409C3×C22⋊C4—22no—
410C3×C22⋊C4—22no—
411C3×C22⋊C4—22no—
412C3×C22⋊C4—22no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—21no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425#217—21no—
426#217—21no—
427#216—41no—
428#215—41no—
429#214—41no—
430#213—41no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433C4⋊Dic3—21no—
434C4⋊Dic3C23×C311yescharacteristic
435C4⋊Dic3C23×C311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438#208—41no—
439C2×C3⋊C8—41no—
440C2×C3⋊C8C23×C311yescharacteristic
441C2×C3⋊C8C23×C311yescharacteristic
442C2×C3⋊C8C23×C311yescharacteristic
443C2×C3⋊C8C23×C311yescharacteristic
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—41no—
464C32×C4—41no—
465C32×C4—41no—
466C32×C4H(5,𝔽2)11yescharacteristic
467C32×C4H(5,𝔽2)11yescharacteristic
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C2×#41—31no—
472C2×#41C2×C3×D311yescharacteristic
473C2×#41C2×C3×D311yescharacteristic
474C2×Q16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×D8—31no—
478C2×M16—31no—
479C22×C8—31no—
480C22⋊Q8—21no—
481C22⋊Q8—31no—
482C22⋊Q8—31no—
483C22⋊Q8—61no—
484C22⋊Q8C2×C3×D311yescharacteristic
485C22⋊Q8C2×C3×D311yescharacteristic
486#121—21no—
487#121—21no—
488#121—21no—
489#121—31no—
490#121—31no—
491#121—61no—
492#121—61no—
493#121—61no—
494#121C2×C3×D311yescharacteristic
495#121C2×C3×D311yescharacteristic
496C2×C4⋊C4—31no—
497C2×C4⋊C4C2×C3×D311yescharacteristic
498#106—31no—
499#106—31no—
500#106—31no—
501#106—31no—
502#103—31no—
503#103—31no—
504#103—31no—
505#103—31no—
506#102—31no—
507#102—31no—
508#102—31no—
509#102—31no—
510C22⋊C8—31no—
511C22⋊C8—31no—
512C22⋊C8—31no—
513C22⋊C8—31no—
514C23×C3—22no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—61no—
521C23×C3C2×#6711yescharacteristic
522C23×C3C2×#6711yescharacteristic
523C23×C3C2×#6711yescharacteristic
524C23×C3C2×C3×D411yescharacteristic
525C23×C3C2×C3×D411yescharacteristic
526C23×C3C2×C3×D411yescharacteristic
527C22×D3—21no—
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×Q8—41no—
536C3×Q8—42no—
537C3×Q8—61no—
538C3×Q8—61no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—41no—
544C3×D4—41no—
545C3×D4—41no—
546C3×D4—41no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—42no—
552C3×D4—42no—
553C3×D4—42no—
554C3×D4—44no—
555C3×D4—42no—
556C3×D4—42no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—81no—
560C3×D4—81no—
561C3×D4—81no—
562C3×D4—81no—
563C3×D4—82no—
564C3×D4—82no—
565C3×D4—122no—
566C3×D4—241no—
567C3×D4—241no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—44no—
600C2×C3×C4—42no—
601C2×C3×C4—42no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—81no—
606C2×C3×C4—81no—
607C2×C3×C4—82no—
608C2×C3×C4—122no—
609C2×C3×C4—241no—
610C2×C3×C4C2×#6711yescharacteristic
611C2×C3×C4C2×#6711yescharacteristic
612C2×C3×C4C2×#6711yescharacteristic
613C2×C3×C4C2×C3×D411yescharacteristic
614C2×C3×C4C2×C3×D411yescharacteristic
615C2×C3×C4C2×C3×D411yescharacteristic
616C2×C3×C4C23×D311yescharacteristic
617C2×C3×C4C24×C311yescharacteristic
618#67—42no—
619#67—81no—
620#67—81no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—81no—
625D12—21no—
626D12—21no—
627C4×D3—42no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—81no—
642C2×C32#53411yescharacteristic
643C2×C32#57711yescharacteristic
644C2×C32#57711yescharacteristic
645C3×D3—81no—
646#41—41no—
647#41—41no—
648#41—41no—
649#41—41no—
650#41—121no—
651#41—121no—
652C2×Q8—31no—
653C2×Q8C3×#6711yescharacteristic
654C2×Q8C22×C3×D311yescharacteristic
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4C3×#6711yescharacteristic
663C2×D4C3×#6711yescharacteristic
664C2×D4C3×#6711yescharacteristic
665C2×D4C22×C3×D311yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4C22×C3×D311yescharacteristic
671C22×C4C22×C3×D311yescharacteristic
672C22×C4C22×C3×D311yescharacteristic
673Q16—121no—
674SD16—121no—
675SD16—121no—
676D8—121no—
677M16—121no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—121no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—31no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4C22×C3×D311yescharacteristic
692C4⋊C4C22×C3×D311yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22×C3—22no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3C22×#6711yescharacteristic
742C22×C3C22×C3×D411yescharacteristic
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—42no—
758C3×C4—42no—
759C3×C4—42no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4#100411yescharacteristic
770C3×C4#100411yescharacteristic
771C3×C4C3×H(5,𝔽2)11yescharacteristic
772C3×C4C3×H(5,𝔽2)11yescharacteristic
773Dic3—41no—
774Dic3—41no—
775Dic3—41no—
776C32#320411yescharacteristic, complemented, Sylow
777C23—21no—
778C23—61no—
779C23C2×C3×#6711yescharacteristic
780C23C2×C3×#6711yescharacteristic
781C23C2×C3×#6711yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—41no—
785Q8—61no—
786Q8—61no—
787D4—21no—
788D4—21no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—42no—
793D4—61no—
794D4—61no—
795D4—81no—
796D4—81no—
797D4—122no—
798D4—241no—
799D4—241no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—42no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—81no—
814C2×C4—122no—
815C2×C4—241no—
816C2×C4C2×C3×#6711yescharacteristic
817C2×C4C2×C3×#6711yescharacteristic
818C2×C4C2×C3×#6711yescharacteristic
819C2×C4C23×C3×D311yescharacteristic
820C8—61no—
821C8—61no—
822C8—61no—
823C8—61no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—82no—
837C2×C3—81no—
838C2×C3—81no—
839C2×C3—241no—
840C2×C3#580411yescharacteristic
841C2×C3#583611yescharacteristic
842C2×C3#583711yescharacteristic
843C2×C3C3×#53411yescharacteristic
844C2×C3C3×#57711yescharacteristic
845C2×C3C3×#57711yescharacteristic
846D3—81no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22C22×C3×#6711yescharacteristic
863C4—21no—
864C4—21no—
865C4—21no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—121no—
870C4—121no—
871C4—121no—
872C4C3×#100411yescharacteristic
873C4C3×#100411yescharacteristic
874C3—21no—
875C3#8342911yescharacteristic, direct product factor
876C3C3×#320411yescharacteristic, complemented
877C2—41no—
878C2—41no—
879C2—41no—
880C2—81no—
881C2—241no—
882C2C3×#580411yescharacteristic
883C2C3×#583611yescharacteristic
884C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#537C2
socleC22×C32C22×D4
hypercenterC3×#537D3
hypocenterC3C3×#3204
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
1. C32×#537C2semidirect
2. C3×#5833C2semidirect
3. C3×#5239C2semidirect
4. C3×#5238C2semidirect
5. C3×#5234C2semidirect
6. C3×#5052C2semidirect
7. C3×#5048C2semidirect
8. C3×#5047C2semidirect
9. C3×#5043C2semidirect
10. C3×#5041C2semidirect
11. C3×#5039C2semidirect
12. C3×#5037C2semidirect
13. C3×#5034C2semidirect
14. C3×#4971C2semidirect
15. C3×#4968C2semidirect
17. #83429C3direct (N × H)
63. C3×#537D3semidirect
64. C3×#537C2×C3semidirect
65. #5833C2×C3semidirect
79. #5239C2×C3semidirect
80. #5238C2×C3semidirect
81. #5234C2×C3semidirect
82. #5052C2×C3semidirect
83. #5048C2×C3semidirect
84. #5047C2×C3semidirect
85. #5043C2×C3semidirect
86. #5041C2×C3semidirect
87. #5039C2×C3semidirect
88. #5037C2×C3semidirect
89. #5034C2×C3semidirect
90. #4971C2×C3semidirect
91. #4968C2×C3semidirect
293. #537C3×D3semidirect
776. C32#3204semidirect
875. C3#83429direct (N × H)
876. C3C3×#3204semidirect

Maximal subgroups

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

subgroupindex
C32×#5372
C3×#58332
C3×#52392
C3×#52382
C3×#52342
C3×#50522
C3×#50482
C3×#50472
C3×#50432
C3×#50412
C3×#50392
C3×#50372
C3×#50342
C3×#49712
C3×#49682
C3×#32043
#834293