Finite Group Databasebeta

← #13168672

Subgroups — #13168672

Order 1728.

1238 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723696C211yesmaximal, characteristic
2#11723501C211yesmaximal, characteristic, complemented
3C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
4#11723397C211yesmaximal, characteristic, complemented
5C3×#63871C211yesmaximal, characteristic, complemented
6C3×#63869C211yesmaximal, characteristic, complemented
7C3×#63864C211yesmaximal, characteristic, complemented
8#11723027C212yesmaximal, complemented
9#11722997C212yesmaximal, complemented
10#11722938C212yesmaximal, complemented
11#11722921C212yesmaximal, complemented
12#10595377—31nomaximal
13#10594453—31nomaximal
14#10593943—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6295C2212yes—
19C2×Dic3×C3⋊D3C2212yes—
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×Dic3×C3⋊D3C2211yescharacteristic
22C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88814C2212yes—
27Dic3⋊(C3⋊Dic3)C2212yes—
28#88803C2212yes—
29Dic3×C3⋊Dic3C2211yescharacteristic
30Dic3×C3⋊Dic3C2212yes—
31Dic3×C3⋊Dic3C2211yescharacteristic
32C3×#3724C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×#3722C2212yes—
36C3×#3722C2212yes—
37C3×#3722C2212yes—
38Q8×C3⋊Dic3—31no—
39#64102—31no—
40C42×C3⋊D3—31no—
41C3×#947—31no—
42C3×#946—31no—
43C3×#897—31no—
44C3×#890—31no—
45C3×#875—31no—
46C3×#870—31no—
47#63916—31no—
48#63909—31no—
49#63908—31no—
50#63902—32no—
51#63898—31no—
52#63898—31no—
53#63898—61no—
54#63891—32no—
55#63890—32no—
56#63881—32no—
57#63881—32no—
58#63878—32no—
59#63878—32no—
60C4×D3×Dic3—31no—
61C4×D3×Dic3—31no—
62C4×D3×Dic3—61no—
63#63871D311yescharacteristic, complemented
64#63869D311yescharacteristic, complemented
65#63864D311yescharacteristic, complemented
66#63862—32no—
67#63861—32no—
68#63853—32no—
69#63849—32no—
70#63848—32no—
71#63843—31no—
72#63843—31no—
73#63843—61no—
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)—22no—
82C3×C4×C3⋊D3—22no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×Dic6—22no—
88#6295—24no—
89Dic3×C3⋊D3—22no—
90Dic3×C3⋊D3—22no—
91Dic3×C3⋊D3—24no—
92#5691—91no—
93#5680—91no—
94#5624—91no—
95C2×C32×Q8—31no—
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4×C3⋊D3—31no—
98C2×C4×C3⋊D3—31no—
99C2×C4×C3⋊D3—32no—
100C2×C4×C3⋊D3C2×D311yescharacteristic
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—61no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—61no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2×D311yescharacteristic
109C2×C3×Dic6C2×D311yescharacteristic
110C2×#626—32no—
111C2×#626—32no—
112C2×#625—32no—
113C2×D3×Dic3—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—32no—
118C2×D3×Dic3—32no—
119C2×D3×Dic3—61no—
120C2×D3×Dic3—61no—
121C2×D3×Dic3—62no—
122C32×C4⋊C4—31no—
123C32×C42—31no—
124#3752—32no—
125C4⋊(C3⋊Dic3)—32no—
126C4⋊(C3⋊Dic3)C2×D311yescharacteristic
127C4×C3⋊Dic3—31no—
128C4×C3⋊Dic3—31no—
129C4×C3⋊Dic3—31no—
130C4×C3⋊Dic3—31no—
131C4×C3⋊Dic3—31no—
132C4×C3⋊Dic3—32no—
133C4×C3⋊Dic3—61no—
134C4×C3⋊Dic3—61no—
135C4×C3⋊Dic3—61no—
136C4×C3⋊Dic3—121no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×(C2×D3)⋊C4—32no—
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3—32no—
148C3×C4⋊Dic3—61no—
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×C4⋊Dic3C2×D311yescharacteristic
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3C2×D311yescharacteristic
157C3×C4×Dic3C2×D311yescharacteristic
158#3724C2×D312yes—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3C2×D312yes—
163Dic3⋊Dic3C2×D312yes—
164#3722—32no—
165#3722C2×D312yes—
166#3722C2×D312yes—
167#3722C2×D312yes—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—62no—
173Dic32—32no—
174Dic32—32no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—62no—
180Dic32—61no—
181Dic32—61no—
182C22×C33C2411yescharacteristic
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3#4112yes—
189C33×C4#4112yes—
190C3⋊(C3⋊Dic3)—21no—
191C3⋊(C3⋊Dic3)#4112yes—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—22no—
194C32×Dic3—21no—
195C32×Dic3—21no—
196C32×Dic3—22no—
197C32×Dic3—22no—
198C3×#125—91no—
199C3×#124—91no—
200C3×C22⋊Q8—91no—
201#947—31no—
202#946—31no—
203Q8×Dic3—91no—
204Q8×Dic3—91no—
205Q8×Dic3—181no—
206#938—91no—
207D4×Dic3—91no—
208#930—91no—
209C2×C4×Dic3—91no—
210#898—92no—
211#898—92no—
212#897—31no—
213#895—91no—
214#894—92no—
215#893—92no—
216#893—91no—
217#893—91no—
218#893—181no—
219#892—92no—
220#892—92no—
221#890—31no—
222#887—91no—
223#886—92no—
224#883—92no—
225#67⋊C4—92no—
226#67⋊C4—92no—
227#879—92no—
228#877—92no—
229#875—31no—
230C42×D3—91no—
231C42×D3—91no—
232C42×D3—181no—
233#870—31no—
234C22×C3⋊D3C22×D312yes—
235C22×C3⋊D3C22×D311yescharacteristic
236C22×C3×D3—31no—
237C22×C3×D3—31no—
238C22×C3×D3—32no—
239C22×C3×D3—32no—
240C22×C3×D3—61no—
241C22×C3×D3—62no—
242C32×Q8—62no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—31no—
247C2×C32×C4—31no—
248C2×C32×C4—32no—
249C2×C32×C4—32no—
250C2×C32×C4—41no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—61no—
262C2×C3⋊Dic3—61no—
263C2×C3⋊Dic3—61no—
264C2×C3⋊Dic3—61no—
265C2×C3⋊Dic3—61no—
266C2×C3⋊Dic3—121no—
267C2×C3⋊Dic3—121no—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D312yes—
270C4⋊(C3⋊D3)—22no—
271C4×C3⋊D3—22no—
272C4×C3⋊D3—62no—
273C4×C3⋊D3—62no—
274C4×C3⋊D3—64no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C3×D12—64no—
294C3×D12—62no—
295C3×D12—62no—
296C3×C4×D3—64no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×Dic6—24no—
300C3×Dic6—22no—
301C3×Dic6—22no—
302#626—64no—
303#626—64no—
304#625—64no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307D3×Dic3—64no—
308D3×Dic3—64no—
309D3×Dic3—62no—
310D3×Dic3—62no—
311D3×Dic3—64no—
312D3×Dic3—64no—
313D3×Dic3—124no—
314#529—271noSylow
315C2×C33C2×#4111yescharacteristic
316C2×C33C2×#4111yescharacteristic
317C2×C33C2×#4111yescharacteristic
318C3×C3⋊D3—22no—
319C3×C3⋊D3—42no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×D4—91no—
324C22×C3×C4—91no—
325C2×#67—92no—
326C2×#67—92no—
327C22×Dic3—92no—
328C22×Dic3—91no—
329C22×Dic3—91no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—92no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—92no—
342C2×C4×D3—92no—
343C2×C4×D3—181no—
344C2×C4×D3—181no—
345C2×C4×D3—182no—
346C2×Dic6D3211yescharacteristic
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—92no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4—91no—
354C3×C22⋊C4—92no—
355C3×C22⋊C4—92no—
356C3×C22⋊C4—92no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360#217—92no—
361#217—92no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4—32no—
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—32no—
366(C2×D3)⋊C4—32no—
367(C2×D3)⋊C4—32no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—92no—
370(C2×D3)⋊C4—92no—
371(C2×D3)⋊C4—92no—
372(C2×D3)⋊C4—182no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—32no—
376C4⋊Dic3—32no—
377C4⋊Dic3—61no—
378C4⋊Dic3—92no—
379C4⋊Dic3—92no—
380C4⋊Dic3—182no—
381C4⋊Dic3D3211yescharacteristic
382Dic3⋊C4—32no—
383Dic3⋊C4—32no—
384Dic3⋊C4—32no—
385Dic3⋊C4—32no—
386Dic3⋊C4—92no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—92no—
392C4×Dic3—92no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—92no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—181no—
400C4×Dic3—181no—
401C4×Dic3—182no—
402C4×Dic3—181no—
403C4×Dic3—181no—
404C4×Dic3—181no—
405C4×Dic3—361no—
406C4×Dic3D3211yescharacteristic
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—41no—
411C22×C32C23×D311yescharacteristic
412C22×C32C23×D311yescharacteristic
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—22no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—22no—
419C2×C3⋊D3#23912yes—
420C2×C3×D3—32no—
421C2×C3×D3—32no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—62no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3—61no—
429C2×C3×D3—64no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—122no—
437C2×C3×D3—122no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—22no—
441C32×C4—42no—
442C32×C4—61no—
443C32×C4—62no—
444C32×C4—61no—
445C32×C4—62no—
446C32×C4#23712yes—
447C32×C4#23712yes—
448C32×C4#23912yes—
449C3⋊Dic3—21no—
450C3⋊Dic3—22no—
451C3⋊Dic3—32no—
452C3⋊Dic3—32no—
453C3⋊Dic3—32no—
454C3⋊Dic3—62no—
455C3⋊Dic3—62no—
456C3⋊Dic3—62no—
457C3⋊Dic3—61no—
458C3⋊Dic3—62no—
459C3⋊Dic3—61no—
460C3⋊Dic3—61no—
461C3⋊Dic3—122no—
462C3⋊Dic3—121no—
463C3⋊Dic3—121no—
464C3⋊Dic3—122no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—24no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—21no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—42no—
477C3×Dic3—62no—
478C3×Dic3—61no—
479C3×Dic3—62no—
480C3×Dic3—61no—
481C3×Dic3—62no—
482C3×Dic3—122no—
483#126—272no—
484#125—91no—
485#124—91no—
486#123—272no—
487C22⋊Q8—91no—
488#121—271no—
489C4×Q8—271no—
490C4×D4—272no—
491C4×D4—271no—
492#117—272no—
493C2×C42—271no—
494C33#52911yescharacteristic, complemented, Sylow
495C23×C3—91no—
496C23×C3—92no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—61no—
502C22×D3—62no—
503C3×Q8—64no—
504C3×Q8—62no—
505C3×Q8—62no—
506C3×D4—182no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—62no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—62no—
523C2×C3×C4—91no—
524C2×C3×C4—92no—
525C2×C3×C4—182no—
526C2×C3×C4C2×D3211yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529#67—184no—
530#67—184no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—61no—
536C2×Dic3—62no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—181no—
544C2×Dic3—181no—
545C2×Dic3—181no—
546C2×Dic3—181no—
547C2×Dic3—181no—
548C2×Dic3—181no—
549C2×Dic3—182no—
550C2×Dic3—184no—
551C2×Dic3—182no—
552C2×Dic3—361no—
553C2×Dic3—361no—
554C2×Dic3C2×D3211yescharacteristic
555C2×Dic3C2×D3211yescharacteristic
556C2×Dic3C2×D3212yes—
557C2×Dic3C2×D3212yes—
558D12—64no—
559D12—62no—
560D12—62no—
561D12—184no—
562C4×D3—64no—
563C4×D3—62no—
564C4×D3—62no—
565C4×D3—182no—
566C4×D3—182no—
567C4×D3—184no—
568C4×D3—184no—
569C4×D3—182no—
570C4×D3—182no—
571C4×D3—184no—
572C4×D3—184no—
573C4×D3—364no—
574Dic6—22no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32C2×#23711yescharacteristic
588C2×C32C2×#23711yescharacteristic
589C2×C32C2×#23911yescharacteristic
590C2×C32C2×#23911yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C2×C32D3×#4111yescharacteristic
594C2×C32D3×#4111yescharacteristic
595C2×C32D3×#4111yescharacteristic
596C3⋊D3—22no—
597C3⋊D3—42no—
598C3×D3—64no—
599C3×D3—62no—
600C3×D3—62no—
601C3×D3—124no—
602C3×D3—122no—
603C3×D3—122no—
604C2×Q8—31no—
605C2×D4—91no—
606C2×D4—272no—
607C22×C4—91no—
608C22×C4—271no—
609C22×C4—271no—
610C22×C4—272no—
611C4⋊C4—31no—
612C4⋊C4—92no—
613C4⋊C4—92no—
614C4⋊C4—92no—
615C4⋊C4—91no—
616C4⋊C4—272no—
617C22⋊C4—92no—
618C22⋊C4—92no—
619C22⋊C4—92no—
620C22⋊C4—272no—
621C22⋊C4—272no—
622C42—31no—
623C42—271no—
624C42—271no—
625C42—272no—
626C42—271no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—92no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3—182no—
635C22×C3—182no—
636C22×C3—182no—
637C22×C3C22×D3211yescharacteristic
638C22×C3C22×D3211yescharacteristic
639C22×C3C22×D3211yescharacteristic
640C2×D3—32no—
641C2×D3—32no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—64no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—122no—
657C2×D3—122no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—42no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—64no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—62no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—122no—
674C3×C4—181no—
675C3×C4—182no—
676C3×C4#379612yes—
677C3×C4#379612yes—
678C3×C4#380512yes—
679Dic3—21no—
680Dic3—21no—
681Dic3—22no—
682Dic3—22no—
683Dic3—62no—
684Dic3—61no—
685Dic3—62no—
686Dic3—62no—
687Dic3—61no—
688Dic3—92no—
689Dic3—92no—
690Dic3—92no—
691Dic3—122no—
692Dic3—182no—
693Dic3—182no—
694Dic3—182no—
695Dic3—182no—
696Dic3—181no—
697Dic3—181no—
698Dic3—181no—
699Dic3—362no—
700Dic3—361no—
701Dic3—361no—
702Dic3—362no—
703C32—21no—
704C32—21no—
705C32—21no—
706C32—41no—
707C32#562411yescharacteristic, complemented
708C32#568011yescharacteristic, complemented
709C32#569111yescharacteristic, complemented
710C23—91no—
711C23—92no—
712Q8—62no—
713D4—182no—
714D4—544no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—91no—
720C2×C4—92no—
721C2×C4—182no—
722C2×C4—271no—
723C2×C4—271no—
724C2×C4—542no—
725C2×C4—544no—
726C2×C4—542no—
727C2×C4D3311yescharacteristic
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—41no—
740C2×C3—182no—
741C2×C3—362no—
742C2×C3C2×#379611yescharacteristic
743C2×C3C2×#379611yescharacteristic
744C2×C3#6430611yescharacteristic
745C2×C3#6430611yescharacteristic
746C2×C3#6431211yescharacteristic
747C2×C3D3×#23911yescharacteristic
748C2×C3D3×#23911yescharacteristic
749C2×C3#6431911yescharacteristic
750C2×C3C2×#380511yescharacteristic
751D3—64no—
752D3—62no—
753D3—62no—
754D3—124no—
755D3—122no—
756D3—122no—
757C22—92no—
758C22—181no—
759C22—181no—
760C22—182no—
761C22—182no—
762C22—182no—
763C22C2×D3311yescharacteristic
764C4—61no—
765C4—62no—
766C4—61no—
767C4—62no—
768C4—182no—
769C4—181no—
770C4—272no—
771C4—541no—
772C4#8896412yes—
773C3—21no—
774C3—21no—
775C3—21no—
776C3—41no—
777C3#1059394311yescharacteristic, complemented
778C3#1059445311yescharacteristic, complemented
779C3#1059537711yescharacteristic, complemented
780C2—182no—
781C2—362no—
782C2#1172437611yescharacteristic
783C2#1172439111yescharacteristic
784C2C2×#8896411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723696C2
hypercenterC2×C4D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723501C2semidirect
3. C4×Dic3×C3⋊D3C2semidirect
4. #11723397C2semidirect
5. C3×#63871C2semidirect
6. C3×#63869C2semidirect
7. C3×#63864C2semidirect
8. #11723027C2semidirect
9. #11722997C2semidirect
10. #11722938C2semidirect
11. #11722921C2semidirect
63. #63871D3semidirect
64. #63869D3semidirect
65. #63864D3semidirect
494. C33#529semidirect
707. C32#5624semidirect
708. C32#5680semidirect
709. C32#5691semidirect
777. C3#10593943semidirect
778. C3#10594453semidirect
779. C3#10595377semidirect

Maximal subgroups

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

subgroupindex
#117236962
#117235012
C4×Dic3×C3⋊D32
#117233972
C3×#638712
C3×#638692
C3×#638642
#117230272
#117229972
#117229382
#117229212
#105953773
#105944533
#105939433