Finite Group Databasebeta

← #13168641

Subgroups — #13168641

Order 1728.

1112 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6295C211yesmaximal, characteristic
2#11723431C211yesmaximal, characteristic, complemented
3#11723431C211yesmaximal, characteristic, complemented
4#11723406C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×#63872C211yesmaximal, characteristic, complemented
7C3×#63849C211yesmaximal, characteristic, complemented
8#11723027C212yesmaximal, complemented
9#11723011C212yesmaximal, complemented
10#11722995C212yesmaximal
11#11722915C212yesmaximal, complemented
12#10594584—31nomaximal
13#10594553—31nomaximal
14#10594550—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6295C2211yescharacteristic
19C2×C3×#624C2212yes—
20C3×C4×C3⋊Dic3C2211yescharacteristic
21C32×C4⋊Dic3C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24#88815C2211yescharacteristic
25#88814C2211yescharacteristic
26#88814C2211yescharacteristic
27#88806C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30#88803C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38#64106—31no—
39#64106—31no—
40#64096—31no—
41C3×#892—31no—
42C3×#892—31no—
43C3×D3×C4⋊C4—31no—
44C3×D3×C4⋊C4—31no—
45C3×#890—31no—
46C3×#890—31no—
47#63905—32no—
48C4×#626—31no—
49C4×#626—31no—
50C4×#625—31no—
51#63900D311yescharacteristic, complemented
52#63872D311yescharacteristic, complemented
53#63869—32no—
54#63867—32no—
55#63862—32no—
56#63861—32no—
57#63857—31no—
58#63857—31no—
59#63857—31no—
60#63857—31no—
61#63857—61no—
62#63857—61no—
63#63855—32no—
64#63854—32no—
65#63850—32no—
66#63849D311yescharacteristic, complemented
67#63848—32no—
68#63845—32no—
69#63844—31no—
70#63844—31no—
71#63844—61no—
72#63841—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308—22no—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C3×C4×C3⋊D3—22no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88#6295—22no—
89C3×#624—24no—
90#5694—91no—
91#5529—91no—
92#5513—91no—
93C2×C4×C3⋊D3C2×D311yescharacteristic
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×#634—31no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—121no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—61no—
109C2×C3×C4×D3—61no—
110C2×#626—31no—
111C2×#626—31no—
112C2×#625—31no—
113C2×#624C2×D312yes—
114C32×C4⋊C4—31no—
115C32×C4⋊C4—31no—
116C32×C4⋊C4—31no—
117#3752—32no—
118#3752—32no—
119C4⋊(C3⋊Dic3)—32no—
120C4⋊(C3⋊Dic3)—32no—
121#3750—32no—
122C4×C3⋊Dic3—32no—
123C4×C3⋊Dic3C2×D311yescharacteristic
124C3×(C2×D3)⋊C4—32no—
125C3×(C2×D3)⋊C4—32no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—32no—
130C3×C4⋊Dic3—32no—
131C3×C4⋊Dic3C2×D311yescharacteristic
132C3×C4⋊Dic3C2×D311yescharacteristic
133C3×C4⋊Dic3C2×D311yescharacteristic
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—32no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—61no—
146#3724—31no—
147#3724—32no—
148#3724—32no—
149#3724—62no—
150#3724C2×D312yes—
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—62no—
158Dic3⋊Dic3—62no—
159Dic3⋊Dic3C2×D312yes—
160Dic3⋊Dic3C2×D312yes—
161#3722—31no—
162#3722—31no—
163#3722C2×D312yes—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
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—
173(C2×D3)⋊Dic3—62no—
174Dic32—32no—
175Dic32—32no—
176Dic32—62no—
177Dic32C2×D312yes—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3#4112yes—
185C33×C4#4112yes—
186C3⋊(C3⋊Dic3)—22no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C32×Dic3—22no—
192C32×Dic3—22no—
193C32×Dic3—22no—
194C3×#125—91no—
195C3×#117—91no—
196C2×C3×C4⋊C4—91no—
197#929—92no—
198C4×#67—91no—
199C4×#67—91no—
200#926—92no—
201#924—91no—
202#924—91no—
203#898—92no—
204#898—92no—
205#897—91no—
206#897—91no—
207#897—91no—
208#897—91no—
209#897—181no—
210#897—181no—
211#894—92no—
212#892—31no—
213#892—31no—
214#892—92no—
215D3×C4⋊C4—31no—
216D3×C4⋊C4—31no—
217#890—31no—
218#890—31no—
219#890—92no—
220#889—92no—
221#887—91no—
222#887—91no—
223#887—181no—
224#883—92no—
225#879—92no—
226C4×D12—91no—
227#872—92no—
228#870—92no—
229C4×Dic6—91no—
230C22×C3⋊D3C22×D311yescharacteristic
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3×D3—31no—
233C22×C3×D3—31no—
234C22×C3×D3—31no—
235C22×C3×D3—31no—
236C22×C3×D3—61no—
237C22×C3×D3—61no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—32no—
242C2×C32×C4—32no—
243C2×C32×C4—32no—
244C2×C32×C4—41no—
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C3⋊Dic3—32no—
249C2×C3⋊Dic3—32no—
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—62no—
252C2×C3⋊Dic3—62no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—122no—
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D311yescharacteristic
259C4×C3⋊D3—22no—
260C4×C3⋊D3—22no—
261#634—62no—
262#634—64no—
263#634—62no—
264#634—62no—
265#634—122no—
266#634—122no—
267#634—124no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C3×C4×D3—64no—
290C3×C4×D3—64no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—122no—
296C3×C4×D3—122no—
297#626—62no—
298#626—62no—
299#625—62no—
300#624—24no—
301#552—271noSylow
302C2×C33C2×#4111yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C332−1+411yescharacteristic
305C3×C3⋊D3—22no—
306C3×C3⋊D3—41no—
307C22×C3×C4—92no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C2×#67—91no—
311C2×#67—91no—
312C2×D12—91no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—32no—
318C2×C4×D3—32no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×Dic6—91no—
322C2×Dic6—91no—
323C2×Dic6—91no—
324C2×Dic6—181no—
325C2×Dic6—181no—
326C2×Dic6—181no—
327C2×Dic6—361no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—92no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C22⋊C4—92no—
341C3×C42—92no—
342C3×C42—91no—
343#217—91no—
344#217—91no—
345#217—92no—
346#217—92no—
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—91no—
351(C2×D3)⋊C4—91no—
352(C2×D3)⋊C4—91no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—182no—
358(C2×D3)⋊C4—182no—
359C4⋊Dic3—32no—
360C4⋊Dic3—32no—
361C4⋊Dic3—91no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365C4⋊Dic3—92no—
366C4⋊Dic3—182no—
367C4⋊Dic3—182no—
368C4⋊Dic3D3211yescharacteristic
369C4⋊Dic3D3211yescharacteristic
370C4⋊Dic3D3211yescharacteristic
371Dic3⋊C4—32no—
372Dic3⋊C4—32no—
373Dic3⋊C4—32no—
374Dic3⋊C4—32no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382Dic3⋊C4—182no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—32no—
386C4×Dic3—32no—
387C4×Dic3—61no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—182no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—41no—
396C22×C32C23×D311yescharacteristic
397C22×C32C23×D311yescharacteristic
398C22×C32C23×D311yescharacteristic
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3#23712yes—
405C2×C3×D3—32no—
406C2×C3×D3—32no—
407C2×C3×D3—62no—
408C2×C3×D3—61no—
409C2×C3×D3—61no—
410C2×C3×D3—61no—
411C2×C3×D3—61no—
412C2×C3×D3—62no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—121no—
420C2×C3×D3—121no—
421C2×C3×D3—121no—
422C2×C3×D3—121no—
423C32×C4—22no—
424C32×C4—22no—
425C32×C4—22no—
426C32×C4—42no—
427C32×C4—62no—
428C32×C4—62no—
429C32×C4—62no—
430C32×C4#23512yes—
431C32×C4#23512yes—
432C32×C4#23912yes—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—62no—
438C3⋊Dic3—64no—
439C3⋊Dic3—62no—
440C3⋊Dic3—62no—
441C3⋊Dic3—122no—
442C3⋊Dic3—122no—
443C3⋊Dic3—124no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—42no—
451C3×Dic3—42no—
452C3×Dic3—42no—
453C3×Dic3—62no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—61no—
462C3×Dic3—121no—
463C3×Dic3—121no—
464C3×Dic3—121no—
465#126—272no—
466#125—91no—
467#125—272no—
468#123—272no—
469C22⋊Q8—271no—
470C22⋊Q8—271no—
471C4×Q8—271no—
472C4×D4—271no—
473#117—91no—
474#117—272no—
475C2×C4⋊C4—91no—
476C33#55211yescharacteristic, complemented, Sylow
477C23×C3—91no—
478C23×C3—91no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C22×D3—61no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—41no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—184no—
503C2×C3×C4—182no—
504C2×C3×C4—182no—
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C2×D3211yescharacteristic
508#67—182no—
509#67—182no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—92no—
523C2×Dic3—92no—
524C2×Dic3—92no—
525C2×Dic3—182no—
526C2×Dic3—182no—
527C2×Dic3—182no—
528C2×Dic3—362no—
529C2×Dic3C2×D3212yes—
530C2×Dic3C2×D3212yes—
531C2×Dic3C2×D3212yes—
532D12—182no—
533C4×D3—64no—
534C4×D3—64no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—62no—
539C4×D3—122no—
540C4×D3—122no—
541Dic6—184no—
542Dic6—182no—
543Dic6—182no—
544Dic6—182no—
545Dic6—362no—
546Dic6—362no—
547Dic6—364no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—41no—
558C2×C32—41no—
559C2×C32—41no—
560C2×C32C2×#23511yescharacteristic
561C2×C32C2×#23511yescharacteristic
562C2×C32C2×#23711yescharacteristic
563C2×C32C2×#23911yescharacteristic
564C2×C32#100711yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C2×C32#101011yescharacteristic
568C2×C32#101011yescharacteristic
569C3⋊D3—22no—
570C3⋊D3—41no—
571C3×D3—62no—
572C3×D3—62no—
573C3×D3—122no—
574C3×D3—122no—
575C3×D3—121no—
576C3×D3—121no—
577C2×Q8—271no—
578C2×D4—271no—
579C22×C4—92no—
580C22×C4—91no—
581C22×C4—91no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—92no—
586C4⋊C4—92no—
587C4⋊C4—92no—
588C4⋊C4—272no—
589C4⋊C4—272no—
590C4⋊C4—272no—
591C4⋊C4—271no—
592C22⋊C4—92no—
593C22⋊C4—272no—
594C22⋊C4—272no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C42—92no—
598C42—91no—
599C42—272no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—41no—
604C22×C3—92no—
605C22×C3—181no—
606C22×C3—181no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3C22×D3211yescharacteristic
611C22×C3C22×D3211yescharacteristic
612C22×C3C22×D3211yescharacteristic
613C2×D3—32no—
614C2×D3—32no—
615C2×D3—62no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—62no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—42no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—62no—
639C3×C4—62no—
640C3×C4—62no—
641C3×C4—122no—
642C3×C4—122no—
643C3×C4—122no—
644C3×C4—181no—
645C3×C4—181no—
646C3×C4—181no—
647C3×C4—181no—
648C3×C4#379812yes—
649C3×C4#379912yes—
650C3×C4#379912yes—
651Dic3—22no—
652Dic3—22no—
653Dic3—22no—
654Dic3—62no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—184no—
667Dic3—182no—
668Dic3—182no—
669Dic3—182no—
670Dic3—362no—
671Dic3—362no—
672Dic3—364no—
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#551311yescharacteristic, complemented
678C32#552911yescharacteristic, complemented
679C32#569411yescharacteristic, complemented
680C23—91no—
681C23—91no—
682Q8—542no—
683D4—542no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—184no—
692C2×C4—182no—
693C2×C4—182no—
694C2×C4—272no—
695C2×C4D3311yescharacteristic
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—182no—
709C2×C3—361no—
710C2×C3C2×#379811yescharacteristic
711C2×C3C2×#379911yescharacteristic
712C2×C3C2×#379911yescharacteristic
713C2×C3#6430911yescharacteristic
714C2×C3D3×#23711yescharacteristic
715C2×C3D3×#23711yescharacteristic
716C2×C3#6431511yescharacteristic
717C2×C3#6431511yescharacteristic
718C2×C3#6431911yescharacteristic
719D3—62no—
720D3—62no—
721D3—122no—
722D3—122no—
723D3—121no—
724D3—121no—
725C22—92no—
726C22—181no—
727C22—181no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22C2×D3311yescharacteristic
732C4—62no—
733C4—62no—
734C4—62no—
735C4—181no—
736C4—181no—
737C4—181no—
738C4—181no—
739C4—542no—
740C4#8896512yes—
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3#1059455011yescharacteristic, complemented
746C3#1059455311yescharacteristic, complemented
747C3#1059458411yescharacteristic, complemented
748C2—182no—
749C2—361no—
750C2#1172437411yescharacteristic
751C2#1172439411yescharacteristic
752C2C2×#8896511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6295C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723431C2semidirect
3. #11723431C2semidirect
4. #11723406C2semidirect
5. C3×#63900C2semidirect
6. C3×#63872C2semidirect
7. C3×#63849C2semidirect
8. #11723027C2semidirect
9. #11723011C2semidirect
11. #11722915C2semidirect
51. #63900D3semidirect
52. #63872D3semidirect
66. #63849D3semidirect
476. C33#552semidirect
677. C32#5513semidirect
678. C32#5529semidirect
679. C32#5694semidirect
745. C3#10594550semidirect
746. C3#10594553semidirect
747. C3#10594584semidirect

Maximal subgroups

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

subgroupindex
C4×#62952
#117234312
#117234062
C3×#639002
C3×#638722
C3×#638492
#117230272
#117230112
#117229952
#117229152
#105945843
#105945533
#105945503