Finite Group Databasebeta

← C3×#80129 #11884822

Subgroups — C3×#80129 #11884822

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5831C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×C3×#915C211yesmaximal, characteristic, complemented
4C3×#5599C211yesmaximal, characteristic, complemented
5C32×#449C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7C3×#5158C211yesmaximal, characteristic, complemented
8C3×#5154C211yesmaximal, characteristic, complemented
9C3×#5041C211yesmaximal, characteristic, complemented
10C3×#4806C211yesmaximal, characteristic, complemented
11C3×#4789C211yesmaximal, characteristic, complemented
12C3×#4782C211yesmaximal, characteristic, complemented
13C3×#4767C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3271—31nomaximal
17#80129C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic
24C32×#121C2211yescharacteristic
25C3×#950—24no—
26C3×Q8×Dic3C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×#940—21no—
30C3×#940C2211yescharacteristic
31C3×#939—21no—
32C3×#938—21no—
33C3×#938C2211yescharacteristic
34C3×#936—21no—
35C3×#936C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#214C2211yescharacteristic
38C2×C3×#213C2211yescharacteristic
39C3×C4×#67—21no—
40C3×C4×#67C2211yescharacteristic
41C3×#924—21no—
42C3×#924C2211yescharacteristic
43C22×C3×C3⋊C8C2211yescharacteristic
44C3×#915—24no—
45C2×C3×Dic12C2211yescharacteristic
46C2×C3×#204C2211yescharacteristic
47C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
48C3×#895C2211yescharacteristic
49C3×#887C2211yescharacteristic
50C3×#884—21no—
51C3×#67⋊C4—21no—
52C32×#103C2211yescharacteristic
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#815C2211yescharacteristic
60C3×Dic3⋊C8C2211yescharacteristic
61C3×#810C2211yescharacteristic
62C3×#808C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#548—31no—
67#5831C2×C311yescharacteristic, complemented
68C2×#950C2×C311yescharacteristic, complemented
69C2×#915C2×C311yescharacteristic, complemented
70#5599C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#469—31no—
73C3×#465—31no—
74C3×#464—31no—
75C3×#460—31no—
76C3×#452—31no—
77C3×#449—21no—
78C3×#449—31no—
79C3×#449D311yescharacteristic, complemented
80C3×#449C2×C311yescharacteristic, complemented
81C3×#448—31no—
82C3×#441—31no—
83C3×#435—31no—
84#5163C2×C311yescharacteristic, complemented
85#5158C2×C311yescharacteristic, complemented
86#5154C2×C311yescharacteristic, complemented
87#5041C2×C311yescharacteristic, complemented
88#4806C2×C311yescharacteristic, complemented
89#4789C2×C311yescharacteristic, complemented
90#4782C2×C311yescharacteristic, complemented
91#4767C2×C311yescharacteristic, complemented
92#4733C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C32×#41—22no—
95C32×#41—41no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C22×C3×Dic3—21no—
110C3×D3×Q8—22no—
111C3×D3×Q8—41no—
112C3×#237—22no—
113C3×#237—41no—
114C3×#235—22no—
115C3×#235—41no—
116C2×C3×D12—21no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124C32×SD16—22no—
125C32×D8—41no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217D411yescharacteristic
135C3×#216D414yescomplemented
136C3×#215—22no—
137C3×#214—22no—
138C3×#214—22no—
139C3×#213—22no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4D411yescharacteristic
147C3×C4×Dic3—21no—
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12—22no—
154C3×#204—41no—
155C3×ΓL(1,𝔽25)—22no—
156#3271—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C22×C311yescharacteristic
162C22×C3×Q8—31no—
163C2×D3×Q8C22×C311yescharacteristic
164C2×#237C22×C311yescharacteristic
165C2×#235C22×C311yescharacteristic
166C3×#137—64no—
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16C2×D311yescharacteristic
176C2×C3×SD16C22×C311yescharacteristic
177C2×C3×D8—21no—
178C2×C3×D8—31no—
179C2×C3×D8C2×D311yescharacteristic
180C2×C3×D8C22×C311yescharacteristic
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×#127—31no—
184C3×#127—61no—
185C3×#124—31no—
186C3×#124—61no—
187C3×C22⋊Q8—31no—
188C3×C22⋊Q8—61no—
189C3×#121—21no—
190C3×#121—31no—
191C3×#121—31no—
192C3×#121—61no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#121C2×D311yescharacteristic
196C3×#121C22×C311yescharacteristic
197C3×C4×Q8—31no—
198C3×C4×Q8—31no—
199C3×C4×D4—31no—
200C3×C4×D4—61no—
201C3×C4×D4—61no—
202#950—24no—
203Q8×Dic3C22×C311yescharacteristic
204C2×#216C22×C311yescharacteristic
205C2×#215C22×C311yescharacteristic
206#940—21no—
207#940C22×C311yescharacteristic
208#939—21no—
209#938—21no—
210#938C22×C311yescharacteristic
211#936—21no—
212#936C22×C311yescharacteristic
213C2×#214C22×C311yescharacteristic
214C2×#214C22×C311yescharacteristic
215C2×#213C22×C311yescharacteristic
216C4×#67—21no—
217C4×#67C22×C311yescharacteristic
218#924—21no—
219#924C22×C311yescharacteristic
220C22×C3⋊C8C22×C311yescharacteristic
221#915—24no—
222C2×Dic12C22×C311yescharacteristic
223C2×#204C22×C311yescharacteristic
224C2×ΓL(1,𝔽25)C22×C311yescharacteristic
225#895C22×C311yescharacteristic
226#887C22×C311yescharacteristic
227#884—21no—
228#67⋊C4—21no—
229C3×#106—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103C2×D311yescharacteristic
235C3×#103C22×C311yescharacteristic
236C3×#102—21no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic
240C3×#102C22×C311yescharacteristic
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic
244C3×C22⋊C8C22×C311yescharacteristic
245C3×#97—31no—
246#832C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249#816C22×C311yescharacteristic
250#815C22×C311yescharacteristic
251Dic3⋊C8C22×C311yescharacteristic
252#810C22×C311yescharacteristic
253#808C22×C311yescharacteristic
254C23×C32—21no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C32×Q8—21no—
260C32×Q8C2×D412yes—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—42no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C3×#67—41no—
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—81no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—42no—
298C3×Dic6C2×D412yes—
299C32×C8—21no—
300C32×C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×#137—31no—
304C2×#135—31no—
305#550—31no—
306#548—31no—
307#496—31no—
308#469—31no—
309#465—31no—
310#464—31no—
311#460—31no—
312#452—31no—
313#449—31no—
314#449C3×D311yescharacteristic, complemented
315#448—31no—
316#441—31no—
317#435—31no—
318C3×#41—22no—
319C3×#41—22no—
320C3×#41—42no—
321C3×#41—41no—
322C3×#41—41no—
323C3×#41—42no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×Q8—61no—
332C2×C3×Q8—62no—
333C2×C3×Q8—121no—
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C23×C311yescharacteristic
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—41no—
345C2×C3×D4—41no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4C22×D311yescharacteristic
353C2×C3×D4C22×D311yescharacteristic
354C2×C3×D4C23×C311yescharacteristic
355C2×C3×D4C23×C311yescharacteristic
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—41no—
361C22×C3×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—21no—
369C2×#67—21no—
370C2×#67—21no—
371C2×#67C3×D411yescharacteristic
372C22×Dic3—21no—
373D3×Q8—22no—
374D3×Q8—41no—
375#237—22no—
376#237—41no—
377#235—22no—
378#235—41no—
379C2×D12—21no—
380C2×D12C23×C311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3C23×C311yescharacteristic
384C2×Dic6—21no—
385C2×Dic6C23×C311yescharacteristic
386C2×Dic6C23×C311yescharacteristic
387C3×Q16—34no—
388C3×Q16—62no—
389C3×SD16—22no—
390C3×SD16—22no—
391C3×SD16—42no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—62no—
395C3×SD16—121no—
396C3×D8—41no—
397C3×D8—41no—
398C3×D8—42no—
399C3×D8—62no—
400C3×M16—62no—
401C2×C3×C8—21no—
402C2×C3×C8—21no—
403C2×C3×C8—31no—
404C2×C3×C8—31no—
405C2×C3×C8—62no—
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C23×C311yescharacteristic
409C2×C3×C8C23×C311yescharacteristic
410C3×C4⋊C4—21no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—31no—
413C3×C4⋊C4—61no—
414C3×C4⋊C4—61no—
415C3×C4⋊C4—61no—
416C3×C4⋊C4C22×D311yescharacteristic
417C3×C4⋊C4C23×C311yescharacteristic
418C3×C22⋊C4—21no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—31no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—41no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C42—31no—
429C3×C42—61no—
430C3×C42—61no—
431#217—21no—
432#217—21no—
433#217—21no—
434#217—21no—
435#217C3×D411yescharacteristic
436#216C3×D414yescomplemented
437#215—22no—
438#214—22no—
439#214—22no—
440#213—22no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4C3×D411yescharacteristic
443C4⋊Dic3—21no—
444C4⋊Dic3C23×C311yescharacteristic
445Dic3⋊C4—21no—
446Dic3⋊C4—21no—
447Dic3⋊C4C3×D411yescharacteristic
448C4×Dic3—21no—
449C4×Dic3—21no—
450C4×Dic3C23×C311yescharacteristic
451C2×C3⋊C8—22no—
452C2×C3⋊C8C23×C311yescharacteristic
453C2×C3⋊C8C23×C311yescharacteristic
454Dic12—22no—
455#204—41no—
456ΓL(1,𝔽25)—22no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C32×C4—22no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3×Dic3—22no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C2×#41—31no—
485C2×#41—31no—
486C2×#41C2×C3×D311yescharacteristic
487C22×Q8—31no—
488#137—64no—
489#135—64no—
490C2×Q16—31no—
491C2×Q16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×SD16C2×C3×D311yescharacteristic
497C2×D8—31no—
498C2×D8C2×C3×D311yescharacteristic
499C2×M16—31no—
500C22×C8—31no—
501#127—31no—
502#127—61no—
503#124—31no—
504#124—61no—
505C22⋊Q8—31no—
506C22⋊Q8—61no—
507#121—31no—
508#121—31no—
509#121—61no—
510#121—61no—
511#121—61no—
512#121C2×C3×D311yescharacteristic
513C4×Q8—31no—
514C4×Q8—31no—
515C4×D4—31no—
516C4×D4—61no—
517C4×D4—61no—
518#106—31no—
519C4⋊C8—31no—
520#103—31no—
521#103—31no—
522#103C2×C3×D311yescharacteristic
523#102—31no—
524#102—31no—
525#102C2×C3×D311yescharacteristic
526C22⋊C8—31no—
527C22⋊C8C2×C3×D311yescharacteristic
528#97—31no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3D3×D411yescharacteristic
539C23×C3C2×C3×D411yescharacteristic
540C22×D3—21no—
541C22×D3C2×C3×D411yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—22no—
545C3×Q8—32no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—122no—
551C3×Q8D3×D412yes—
552C3×Q8C2×C3×D412yes—
553C3×D4—22no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—42no—
566C3×D4—42no—
567C3×D4—44no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—81no—
571C3×D4—81no—
572C3×D4—82no—
573C3×D4—121no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—241no—
579C3×D4—241no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—42no—
598C2×C3×C4—42no—
599C2×C3×C4—44no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4—122no—
607C2×C3×C4—122no—
608C2×C3×C4D3×D411yescharacteristic
609C2×C3×C4C2×C3×D411yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C24×C311yescharacteristic
612#67—41no—
613#67—42no—
614#67—42no—
615#67—42no—
616#67—42no—
617#67—81no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—42no—
622C2×Dic3C2×C3×D411yescharacteristic
623C2×Dic3C2×C3×D411yescharacteristic
624C2×Dic3C2×C3×D411yescharacteristic
625D12—21no—
626D12—21no—
627D12—81no—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—42no—
631C4×D3—42no—
632Dic6—21no—
633Dic6—21no—
634Dic6—21no—
635Dic6—42no—
636Dic6C2×C3×D412yes—
637C3×C8—21no—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—41no—
644C3×C8—61no—
645C3⋊C8—21no—
646C3⋊C8C2×C3×D412yes—
647C2×C32—41no—
648C2×C32—81no—
649C2×C32—81no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57711yescharacteristic
653C3×D3—41no—
654C3×D3—81no—
655#41—22no—
656#41—41no—
657#41—62no—
658#41—62no—
659#41—121no—
660#41—121no—
661C2×Q8—31no—
662C2×Q8—31no—
663C2×Q8—61no—
664C2×Q8—62no—
665C2×Q8—121no—
666C2×Q8C22×C3×D311yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4C22×C3×D311yescharacteristic
678C2×D4C22×C3×D311yescharacteristic
679C22×C4—21no—
680C22×C4—31no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4C22×C3×D311yescharacteristic
685Q16—34no—
686Q16—62no—
687SD16—22no—
688SD16—62no—
689SD16—62no—
690SD16—62no—
691SD16—121no—
692D8—41no—
693D8—62no—
694M16—62no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—62no—
698C2×C8C22×C3×D311yescharacteristic
699C2×C8C22×C3×D311yescharacteristic
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4C22×C3×D311yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—31no—
708C22⋊C4—31no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C42—31no—
715C42—61no—
716C42—61no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—42no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C22×C3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C3×C4—21no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—41no—
766C3×C4—42no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—62no—
773C3×C4—81no—
774C3×C4—121no—
775C3×C4—121no—
776C3×C4C2×D3×D411yescharacteristic
777C3×C4#100411yescharacteristic
778C3×C4C22×C3×D411yescharacteristic
779C3×C4C3×H(5,𝔽2)11yescharacteristic
780Dic3—21no—
781Dic3—21no—
782Dic3—22no—
783Dic3—21no—
784Dic3—41no—
785Dic3—41no—
786C32#327111yescharacteristic, complemented, Sylow
787C23—21no—
788C23—21no—
789C23—31no—
790C23—61no—
791C23C3×D3×D411yescharacteristic
792Q8—21no—
793Q8—32no—
794Q8—61no—
795Q8—61no—
796Q8—61no—
797Q8—122no—
798Q8C3×D3×D412yes—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—21no—
803D4—42no—
804D4—61no—
805D4—61no—
806D4—81no—
807D4—121no—
808D4—122no—
809D4—122no—
810D4—122no—
811D4—122no—
812D4—241no—
813D4—241no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—42no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—122no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4C3×D3×D411yescharacteristic
831C2×C4C23×C3×D311yescharacteristic
832C8—21no—
833C8—21no—
834C8—32no—
835C8—61no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—81no—
842C2×C3—82no—
843C2×C3—81no—
844C2×C3—81no—
845C2×C3—81no—
846C2×C3—81no—
847C2×C3—121no—
848C2×C3—161no—
849C2×C3—241no—
850C2×C3#559011yescharacteristic
851C2×C3#576811yescharacteristic
852C2×C3#577511yescharacteristic
853C2×C3C3×D4211yescharacteristic
854C2×C3C3×#57511yescharacteristic
855C2×C3C3×#57711yescharacteristic
856D3—41no—
857D3—81no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22C2×C3×D3×D411yescharacteristic
874C4—21no—
875C4—22no—
876C4—41no—
877C4—61no—
878C4—61no—
879C4—61no—
880C4—62no—
881C4—121no—
882C4—121no—
883C4C2×C3×D3×D411yescharacteristic
884C4C3×#100411yescharacteristic
885C3—21no—
886C3#8012911yescharacteristic, direct product factor
887C3C3×#327111yescharacteristic, complemented
888C2—41no—
889C2—81no—
890C2—81no—
891C2—121no—
892C2—241no—
893C2C3×#559011yescharacteristic
894C2C3×#576811yescharacteristic
895C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#5831C2semidirect
2. C2×C3×#950C2semidirect
3. C2×C3×#915C2semidirect
4. C3×#5599C2semidirect
5. C32×#449C2semidirect
6. C3×#5163C2semidirect
7. C3×#5158C2semidirect
8. C3×#5154C2semidirect
9. C3×#5041C2semidirect
10. C3×#4806C2semidirect
11. C3×#4789C2semidirect
12. C3×#4782C2semidirect
13. C3×#4767C2semidirect
14. C3×#4733C2semidirect
15. C3×#4730C2semidirect
17. #80129C3direct (N × H)
67. #5831C2×C3semidirect
68. C2×#950C2×C3semidirect
69. C2×#915C2×C3semidirect
70. #5599C2×C3semidirect
79. C3×#449D3semidirect
80. C3×#449C2×C3semidirect
84. #5163C2×C3semidirect
85. #5158C2×C3semidirect
86. #5154C2×C3semidirect
87. #5041C2×C3semidirect
88. #4806C2×C3semidirect
89. #4789C2×C3semidirect
90. #4782C2×C3semidirect
91. #4767C2×C3semidirect
92. #4733C2×C3semidirect
93. #4730C2×C3semidirect
135. C3×#216D4semidirect
314. #449C3×D3semidirect
436. #216C3×D4semidirect
786. C32#3271semidirect
886. C3#80129direct (N × H)
887. C3C3×#3271semidirect

Maximal subgroups

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

subgroupindex
C3×#58312
C2×C3×#9502
C2×C3×#9152
C3×#55992
C32×#4492
C3×#51632
C3×#51582
C3×#51542
C3×#50412
C3×#48062
C3×#47892
C3×#47822
C3×#47672
C3×#47332
C3×#47302
C3×#32713
#801293