Finite Group Databasebeta

← #13168449

Subgroups — #13168449

Order 1728.

1194 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723696C211yesmaximal, characteristic
2#11723439C211yesmaximal, characteristic, complemented
3#11723431C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×C4×#624C211yesmaximal, characteristic, complemented
7C3×#63869C211yesmaximal, characteristic, complemented
8#11723023C212yesmaximal, complemented
9#11722995C212yesmaximal, complemented
10#11722931C212yesmaximal, complemented
11#11722915C212yesmaximal, complemented
12#10594447—31nomaximal
13#10593976—31nomaximal
14#10593974—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6295C2212yes—
19C2×C3×#624C2212yes—
20C2×C3×#624C2211yescharacteristic
21C2×C3×#624C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88814C2212yes—
27#88806C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29#88803C2212yes—
30#88803C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×#3722C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38#64106—31no—
39#64084—31no—
40C4×#634—31no—
41C3×#893—31no—
42C3×#890—31no—
43C3×C4×D12—31no—
44C3×C42×D3—31no—
45C3×C42×D3—31no—
46C3×#870—31no—
47#63916—31no—
48#63909—31no—
49#63908—31no—
50#63905—32no—
51#63904—32no—
52#63904—32no—
53C4×#625—32no—
54#63894D311yescharacteristic, complemented
55C4×#624D311yescharacteristic, complemented
56#63869D311yescharacteristic, complemented
57#63868—32no—
58#63861—32no—
59#63860—31no—
60#63860—31no—
61#63860—61no—
62#63859—32no—
63#63857—31no—
64#63857—31no—
65#63857—61no—
66#63855—32no—
67#63854—32no—
68#63850—32no—
69#63844—31no—
70#63844—31no—
71#63844—61no—
72#63841—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308—22no—
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×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88#6295—24no—
89C3×#624—22no—
90C3×#624—22no—
91C3×#624—24no—
92#5691—91no—
93#5557—91no—
94#5479—91no—
95C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
96C2×C4×C3⋊D3C2×D311yescharacteristic
97C2×#634—31no—
98C2×#634—31no—
99C2×#634—31no—
100C2×#634—61no—
101C2×#634—61no—
102C2×#634—61no—
103C2×#634—121no—
104C2×C3×D12—31no—
105C2×C3×D12—31no—
106C2×C3×D12—61no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—61no—
116C2×#626—32no—
117C2×#626—32no—
118C2×#625—32no—
119C2×#624C2×D312yes—
120C2×#624C2×D311yescharacteristic
121C2×#624C2×D311yescharacteristic
122C32×C4⋊C4—31no—
123C32×C42—31no—
124C32×C42—31no—
125#3752—32no—
126#3752—32no—
127#3752—32no—
128C4⋊(C3⋊Dic3)—32no—
129C4⋊(C3⋊Dic3)C2×D311yescharacteristic
130#3750—32no—
131C4×C3⋊Dic3—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—61no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×C4×Dic3—21no—
145C3×C4×Dic3—21no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154#3724—32no—
155#3724—32no—
156#3724—62no—
157#3724C2×D312yes—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3C2×D312yes—
162#3722—32no—
163#3722C2×D312yes—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
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—
174(C2×D3)⋊Dic3—62no—
175Dic32—32no—
176Dic32—32no—
177Dic32—62no—
178Dic32C2×D311yescharacteristic
179Dic32C2×D311yescharacteristic
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—22no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C32×Dic3—21no—
192C32×Dic3—22no—
193C32×Dic3—21no—
194C32×Dic3—21no—
195C32×Dic3#4112yes—
196C3×#125—91no—
197C3×C4×D4—91no—
198C2×C3×C42—91no—
199#938—91no—
200#936—91no—
201#930—91no—
202#929—92no—
203C4×#67—92no—
204C4×#67—92no—
205#926—92no—
206#924—91no—
207#898—92no—
208#897—91no—
209#897—91no—
210#897—181no—
211#895—91no—
212#894—92no—
213#893—31no—
214#893—92no—
215#892—92no—
216#890—31no—
217#887—91no—
218#883—92no—
219#879—92no—
220#876—92no—
221#875—91no—
222#875—91no—
223#875—181no—
224C4×D12—31no—
225#872—92no—
226C42×D3—31no—
227C42×D3—31no—
228#870—31no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—181no—
232C22×C3⋊D3C22×D312yes—
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—31no—
235C22×C3×D3—31no—
236C22×C3×D3—32no—
237C22×C3×D3—32no—
238C22×C3×D3—61no—
239C22×C3×D3—62no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—31no—
244C2×C32×C4—31no—
245C2×C32×C4—31no—
246C2×C32×C4—31no—
247C2×C32×C4—32no—
248C2×C32×C4—41no—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—32no—
254C2×C3⋊Dic3—32no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—122no—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D312yes—
261C4⋊(C3⋊D3)—22no—
262C4×C3⋊D3—22no—
263#634—62no—
264#634—64no—
265#634—62no—
266#634—62no—
267#634—122no—
268#634—122no—
269#634—124no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C3×D12—62no—
292C3×D12—62no—
293C3×D12—122no—
294C3×C4×D3—62no—
295C3×C4×D3—64no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—64no—
301C3×C4×D3—62no—
302C3×C4×D3—122no—
303#626—64no—
304#626—64no—
305#625—64no—
306#624—22no—
307#624—22no—
308#624—24no—
309#529—271noSylow
310C2×C33C2×#4111yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C3×C3⋊D3—22no—
314C3×C3⋊D3—42no—
315C2×C3×D4—91no—
316C22×C3×C4—92no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C22×C3×C4—91no—
320C2×#67—92no—
321C2×#67—92no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—92no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—32no—
333C2×C4×D3—32no—
334C2×C4×D3—61no—
335C2×Dic6—91no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C2×Dic6—181no—
340C2×Dic6—181no—
341C2×Dic6—361no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—92no—
346C3×C4⋊C4—92no—
347C3×C4⋊C4—91no—
348C3×C22⋊C4—92no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—91no—
356C3×C42—91no—
357#217—92no—
358#217—92no—
359#217—92no—
360#217—92no—
361(C2×D3)⋊C4—32no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369(C2×D3)⋊C4—92no—
370(C2×D3)⋊C4—92no—
371(C2×D3)⋊C4—182no—
372(C2×D3)⋊C4—182no—
373(C2×D3)⋊C4—182no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
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—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389Dic3⋊C4—182no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—92no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—182no—
398C4×Dic3D3211yescharacteristic
399C4×Dic3D3211yescharacteristic
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—41no—
404C22×C32C23×D311yescharacteristic
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—22no—
411C2×C3⋊D3—22no—
412C2×C3⋊D3#23512yes—
413C2×C3×D3—32no—
414C2×C3×D3—32no—
415C2×C3×D3—62no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—121no—
427C2×C3×D3—121no—
428C2×C3×D3—122no—
429C2×C3×D3—122no—
430C2×C3×D3—122no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—32no—
435C32×C4—42no—
436C32×C4—62no—
437C32×C4—61no—
438C32×C4—61no—
439C32×C4—61no—
440C32×C4#23512yes—
441C32×C4#23512yes—
442C32×C4#23912yes—
443C3⋊Dic3—21no—
444C3⋊Dic3—22no—
445C3⋊Dic3—62no—
446C3⋊Dic3—64no—
447C3⋊Dic3—62no—
448C3⋊Dic3—62no—
449C3⋊Dic3—122no—
450C3⋊Dic3—122no—
451C3⋊Dic3—124no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—22no—
456C3×Dic3—21no—
457C3×Dic3—21no—
458C3×Dic3—21no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—42no—
465C3×Dic3—62no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—62no—
469C3×Dic3—121no—
470C3×Dic3—122no—
471C3×Dic3#23512yes—
472C3×Dic3#23712yes—
473#126—272no—
474#125—91no—
475#124—271no—
476#123—272no—
477C22⋊Q8—271no—
478#121—271no—
479C4×Q8—271no—
480C4×D4—91no—
481C4×D4—272no—
482#117—272no—
483C2×C42—91no—
484C33#52911yescharacteristic, complemented, Sylow
485C23×C3—91no—
486C23×C3—92no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—61no—
492C22×D3—62no—
493C3×D4—182no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—32no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—62no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—92no—
514C2×C3×C4—91no—
515C2×C3×C4—184no—
516C2×C3×C4—182no—
517C2×C3×C4—182no—
518C2×C3×C4—182no—
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522#67—184no—
523#67—184no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—32no—
527C2×Dic3—32no—
528C2×Dic3—62no—
529C2×Dic3—61no—
530C2×Dic3—92no—
531C2×Dic3—92no—
532C2×Dic3—92no—
533C2×Dic3—182no—
534C2×Dic3—182no—
535C2×Dic3—182no—
536C2×Dic3—362no—
537C2×Dic3C2×D3211yescharacteristic
538C2×Dic3C2×D3211yescharacteristic
539C2×Dic3C2×D3211yescharacteristic
540C2×Dic3C2×D3212yes—
541C2×Dic3C2×D3211yescharacteristic
542D12—62no—
543D12—62no—
544D12—122no—
545D12—184no—
546C4×D3—62no—
547C4×D3—64no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—122no—
555Dic6—184no—
556Dic6—182no—
557Dic6—182no—
558Dic6—182no—
559Dic6—362no—
560Dic6—362no—
561Dic6—364no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—41no—
574C2×C32C2×#23511yescharacteristic
575C2×C32C2×#23511yescharacteristic
576C2×C32C2×#23511yescharacteristic
577C2×C32C2×#23511yescharacteristic
578C2×C32C2×#23711yescharacteristic
579C2×C32C2×#23911yescharacteristic
580C2×C32D3×#4111yescharacteristic
581C2×C32D3×#4111yescharacteristic
582C2×C32D3×#4111yescharacteristic
583C3⋊D3—22no—
584C3⋊D3—42no—
585C3×D3—62no—
586C3×D3—62no—
587C3×D3—122no—
588C3×D3—122no—
589C3×D3—122no—
590C3×D3—242no—
591C2×Q8—271no—
592C2×D4—91no—
593C2×D4—272no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—92no—
597C22×C4—91no—
598C4⋊C4—31no—
599C4⋊C4—92no—
600C4⋊C4—92no—
601C4⋊C4—91no—
602C4⋊C4—272no—
603C4⋊C4—272no—
604C22⋊C4—92no—
605C22⋊C4—272no—
606C22⋊C4—272no—
607C22⋊C4—272no—
608C22⋊C4—272no—
609C42—31no—
610C42—31no—
611C42—91no—
612C42—91no—
613C42—272no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—92no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—182no—
622C22×C3—182no—
623C22×C3—182no—
624C22×C3C22×D3211yescharacteristic
625C22×C3C22×D3211yescharacteristic
626C22×C3C22×D3211yescharacteristic
627C2×D3—32no—
628C2×D3—32no—
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—122no—
643C2×D3—122no—
644C2×D3—122no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—32no—
649C3×C4—32no—
650C3×C4—42no—
651C3×C4—62no—
652C3×C4—61no—
653C3×C4—62no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—62no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—122no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—181no—
665C3×C4—182no—
666C3×C4#379812yes—
667C3×C4#379912yes—
668C3×C4#379912yes—
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—22no—
673Dic3—61no—
674Dic3—61no—
675Dic3—62no—
676Dic3—62no—
677Dic3—121no—
678Dic3—122no—
679Dic3—184no—
680Dic3—182no—
681Dic3—182no—
682Dic3—182no—
683Dic3—362no—
684Dic3—362no—
685Dic3—364no—
686Dic3#379512yes—
687C32—21no—
688C32—21no—
689C32—21no—
690C32—41no—
691C32#547911yescharacteristic, complemented
692C32#555711yescharacteristic, complemented
693C32#569111yescharacteristic, complemented
694C23—91no—
695C23—92no—
696Q8—542no—
697D4—182no—
698D4—544no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—32no—
704C2×C4—91no—
705C2×C4—92no—
706C2×C4—182no—
707C2×C4—184no—
708C2×C4—182no—
709C2×C4—182no—
710C2×C4—272no—
711C2×C4D3311yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—41no—
722C2×C3—41no—
723C2×C3—41no—
724C2×C3—182no—
725C2×C3—362no—
726C2×C3C2×#379511yescharacteristic
727C2×C3C2×#379811yescharacteristic
728C2×C3C2×#379911yescharacteristic
729C2×C3C2×#379911yescharacteristic
730C2×C3D3×#23511yescharacteristic
731C2×C3D3×#23511yescharacteristic
732C2×C3D3×#23511yescharacteristic
733C2×C3D3×#23711yescharacteristic
734C2×C3#6431911yescharacteristic
735D3—62no—
736D3—62no—
737D3—122no—
738D3—122no—
739D3—122no—
740D3—242no—
741C22—92no—
742C22—181no—
743C22—181no—
744C22—182no—
745C22—182no—
746C22—182no—
747C22C2×D3311yescharacteristic
748C4—32no—
749C4—61no—
750C4—62no—
751C4—61no—
752C4—61no—
753C4—182no—
754C4—181no—
755C4—542no—
756C4#8896512yes—
757C3—21no—
758C3—21no—
759C3—21no—
760C3—41no—
761C3#1059397411yescharacteristic, complemented
762C3#1059397611yescharacteristic, complemented
763C3#1059444711yescharacteristic, complemented
764C2—182no—
765C2—362no—
766C2D3×#379511yescharacteristic
767C2#1172438911yescharacteristic
768C2C2×#8896511yescharacteristic
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. #11723439C2semidirect
3. #11723431C2semidirect
4. #11723399C2semidirect
5. C3×#63894C2semidirect
6. C3×C4×#624C2semidirect
7. C3×#63869C2semidirect
8. #11723023C2semidirect
9. #11722995C2semidirect
10. #11722931C2semidirect
11. #11722915C2semidirect
54. #63894D3semidirect
55. C4×#624D3semidirect
56. #63869D3semidirect
484. C33#529semidirect
691. C32#5479semidirect
692. C32#5557semidirect
693. C32#5691semidirect
761. C3#10593974semidirect
762. C3#10593976semidirect
763. C3#10594447semidirect

Maximal subgroups

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

subgroupindex
#117236962
#117234392
#117234312
#117233992
C3×#638942
C3×C4×#6242
C3×#638692
#117230232
#117229952
#117229312
#117229152
#105944473
#105939763
#105939743