Finite Group Databasebeta

← #13178723

Subgroups — #13178723

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
1C3×#64155C211yesmaximal, characteristic, complemented
2C3×#64155C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C4×#6295C211yesmaximal, characteristic
5#11723690C212yesmaximal
6#11723689C211yesmaximal, characteristic, complemented
7#11723683C212yesmaximal, complemented
8#11723680C211yesmaximal, characteristic, complemented
9#11723676C212yesmaximal, complemented
10#11723669C212yesmaximal, complemented
11#11723667C211yesmaximal, characteristic, complemented
12#10595380—31nomaximal
13#10595379—31nomaximal
14#10595344—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×#6295C2211yescharacteristic
19C2×#6294C2212yes—
20C3×#3752C2212yes—
21C3×#3752C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×#3750C2212yes—
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2212yes—
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic
37#88813C2212yes—
38#64155D311yescharacteristic, complemented
39#64155D311yescharacteristic, complemented
40Q8×C3⋊Dic3D311yescharacteristic, complemented
41C3×#946—31no—
42C3×#946—31no—
43C3×#946—31no—
44C3×#946—31no—
45C3×#946—61no—
46C3×#946—61no—
47C3×Q8×Dic3—31no—
48C3×Q8×Dic3—31no—
49C3×Q8×Dic3—61no—
50C4×#626—31no—
51C4×#626—31no—
52C4×#625—31no—
53#63900—31no—
54#63891—32no—
55#63890—32no—
56D3×C4⋊Dic3—31no—
57D3×C4⋊Dic3—31no—
58#63878—32no—
59#63877—32no—
60#63872—31no—
61#63869—31no—
62#63869—31no—
63#63868—32no—
64#63862—32no—
65#63859—32no—
66#63854—32no—
67#63849—31no—
68#63847—32no—
69#63846—32no—
70#63845—32no—
71#63841—31no—
72#63841—31no—
73#63836—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C33×Q8—22no—
77C2×C33×C4C2312yes—
78C2×C33×C4C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2312yes—
86C3×C4×C3⋊D3—22no—
87C3×C4×C3⋊D3—22no—
88#6295—22no—
89#6294—24no—
90#5642—91no—
91#5639—91no—
92#5581—91no—
93C2×C32×Q8—21no—
94C2×C32×Q8—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—41no—
97C2×C32×Q8C2×D311yescharacteristic
98C2×C32×Q8C2×D311yescharacteristic
99C2×C32×Q8C2×D311yescharacteristic
100C2×C4×C3⋊D3C2×D311yescharacteristic
101C2×C4×C3⋊D3C2×D311yescharacteristic
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—61no—
107C2×C3×C4×D3—61no—
108C2×#626—31no—
109C2×#626—31no—
110C2×#625—31no—
111C2×#624—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114#3752C2×D312yes—
115#3752C2×D312yes—
116C4⋊(C3⋊Dic3)C2×D311yescharacteristic
117C4⋊(C3⋊Dic3)C2×D311yescharacteristic
118C4⋊(C3⋊Dic3)C2×D312yes—
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120#3750C2×D312yes—
121#3750C2×D312yes—
122C4×C3⋊Dic3C2×D312yes—
123C4×C3⋊Dic3C2×D311yescharacteristic
124C3×(C2×D3)⋊C4—32no—
125C3×(C2×D3)⋊C4—32no—
126C3×(C2×D3)⋊C4—32no—
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—62no—
129C3×(C2×D3)⋊C4—62no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—32no—
132C3×C4⋊Dic3—32no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—62no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3—61no—
141C3×C4⋊Dic3—61no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—62no—
147C3×Dic3⋊C4—62no—
148C3×C4×Dic3—32no—
149C3×C4×Dic3—32no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—61no—
153C3×C4×Dic3—62no—
154#3724—31no—
155#3724—32no—
156#3724—32no—
157#3724—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—32no—
166#3722—31no—
167#3722—32no—
168#3722—31no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
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—22no—
186C33×C4#4112yes—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—22no—
194C3×C22⋊Q8—91no—
195C3×C22⋊Q8—91no—
196C3×C4×Q8—91no—
197#946—31no—
198#946—31no—
199#946—31no—
200#946—31no—
201#946—61no—
202#946—61no—
203Q8×Dic3—31no—
204Q8×Dic3—31no—
205Q8×Dic3—61no—
206C4×#67—91no—
207C4×#67—91no—
208#926—91no—
209C2×C4⋊Dic3—91no—
210#898—92no—
211#894—92no—
212#892—92no—
213#892—91no—
214#892—91no—
215D3×C4⋊C4—91no—
216D3×C4⋊C4—91no—
217#890—91no—
218#890—91no—
219#890—92no—
220#889—92no—
221#889—92no—
222#886—92no—
223#883—92no—
224#879—92no—
225#877—92no—
226#876—92no—
227C4×D12—91no—
228#872—92no—
229#870—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—
238C32×Q8—22no—
239C32×Q8—24no—
240C32×Q8—22no—
241C32×Q8—22no—
242C32×Q8—42no—
243C32×Q8—42no—
244C32×Q8—44no—
245C2×C32×C4—22no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—22no—
250C2×C32×C4—22no—
251C2×C32×C4—41no—
252C2×C32×C4—42no—
253C2×C32×C4C22×D312yes—
254C2×C32×C4C22×D312yes—
255C2×C32×C4C22×D312yes—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D312yes—
266C4×C3⋊D3—22no—
267C4×C3⋊D3—22no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—62no—
289C3×C4×D3—62no—
290C3×C4×D3—62no—
291C3×C4×D3—62no—
292C3×C4×D3—62no—
293C3×C4×D3—122no—
294C3×C4×D3—122no—
295#626—62no—
296#626—62no—
297#625—62no—
298#624—64no—
299D3×Dic3—64no—
300D3×Dic3—64no—
301#552—271noSylow
302C2×C33C2×#4111yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C332−1+411yescharacteristic
305C3×C3⋊D3—22no—
306C3×C3⋊D3—41no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—41no—
311C2×C3×Q8D3211yescharacteristic
312C2×C3×Q8D3211yescharacteristic
313C2×C3×Q8D3211yescharacteristic
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C2×#67—91no—
317C2×#67—91no—
318C22×Dic3—92no—
319C2×D12—91no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—92no—
327C2×C4×D3—92no—
328C3×C4⋊C4—92no—
329C3×C4⋊C4—92no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—92no—
333C3×C4⋊C4—91no—
334C3×C22⋊C4—92no—
335C3×C22⋊C4—92no—
336C3×C42—91no—
337C3×C42—92no—
338#217—91no—
339#217—91no—
340#217—92no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—32no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—32no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—91no—
352(C2×D3)⋊C4—91no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—32no—
356C4⋊Dic3—32no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—62no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—91no—
366C4⋊Dic3—92no—
367C4⋊Dic3—92no—
368C4⋊Dic3—92no—
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—32no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383C4×Dic3—32no—
384C4×Dic3—32no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—62no—
388C4×Dic3—61no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—92no—
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#23912yes—
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—24no—
425C32×C4—22no—
426C32×C4—22no—
427C32×C4—22no—
428C32×C4—22no—
429C32×C4—22no—
430C32×C4—42no—
431C32×C4—42no—
432C32×C4—42no—
433C32×C4—44no—
434C32×C4#23512yes—
435C32×C4#23712yes—
436C32×C4#23712yes—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3⋊Dic3—22no—
441C3⋊Dic3—22no—
442C3⋊Dic3—21no—
443C3⋊Dic3—22no—
444C3×Dic3—62no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—61no—
448C3×Dic3—61no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—61no—
452C3×Dic3—62no—
453C3×Dic3—62no—
454C3×Dic3—61no—
455C3×Dic3—62no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—121no—
460C3×Dic3—121no—
461C3×Dic3—122no—
462C3×Dic3—122no—
463C3×Dic3—122no—
464C3×Dic3—121no—
465#126—272no—
466#125—271no—
467#125—272no—
468#123—272no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471C4×Q8—91no—
472C4×D4—271no—
473#117—272no—
474#117—271no—
475C2×C4⋊C4—271no—
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—
485C3×Q8—24no—
486C3×Q8—22no—
487C3×Q8—22no—
488C3×Q8—22no—
489C3×Q8—42no—
490C3×Q8—42no—
491C3×Q8—44no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—42no—
499C2×C3×C4—41no—
500C2×C3×C4—91no—
501C2×C3×C4—92no—
502C2×C3×C4—92no—
503C2×C3×C4—91no—
504C2×C3×C4—92no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—182no—
508C2×C3×C4—182no—
509C2×C3×C4C2×D3212yes—
510C2×C3×C4C2×D3212yes—
511C2×C3×C4C2×D3212yes—
512C2×C3×C4C2×D3211yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515#67—182no—
516#67—182no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—32no—
526C2×Dic3—32no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—61no—
532C2×Dic3—62no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—62no—
537C2×Dic3—62no—
538C2×Dic3—184no—
539D12—182no—
540C4×D3—62no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—122no—
545C4×D3—122no—
546C4×D3—184no—
547C4×D3—184no—
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×#23711yescharacteristic
562C2×C32C2×#23711yescharacteristic
563C2×C32C2×#23911yescharacteristic
564C2×C32#100711yescharacteristic
565C2×C32#100711yescharacteristic
566C2×C32D3×#4111yescharacteristic
567C2×C32D3×#4111yescharacteristic
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#111311yescharacteristic
578C2×D4—271no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—272no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—92no—
585C4⋊C4—91no—
586C4⋊C4—92no—
587C4⋊C4—92no—
588C4⋊C4—272no—
589C4⋊C4—272no—
590C4⋊C4—271no—
591C4⋊C4—272no—
592C22⋊C4—92no—
593C22⋊C4—92no—
594C22⋊C4—271no—
595C22⋊C4—272no—
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—24no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—44no—
641C3×C4—42no—
642C3×C4—181no—
643C3×C4—182no—
644C3×C4—182no—
645C3×C4—182no—
646C3×C4—181no—
647C3×C4—181no—
648C3×C4—181no—
649C3×C4#380412yes—
650C3×C4#380412yes—
651C3×C4#380512yes—
652Dic3—62no—
653Dic3—61no—
654Dic3—62no—
655Dic3—62no—
656Dic3—61no—
657Dic3—62no—
658Dic3—62no—
659Dic3—61no—
660Dic3—62no—
661Dic3—62no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—121no—
668Dic3—121no—
669Dic3—122no—
670Dic3—122no—
671Dic3—122no—
672Dic3—121no—
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#558111yescharacteristic, complemented
678C32#563911yescharacteristic, complemented
679C32#564211yescharacteristic, complemented
680C23—91no—
681C23—91no—
682Q8—22no—
683D4—542no—
684C2×C4—91no—
685C2×C4—92no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—92no—
689C2×C4—92no—
690C2×C4—91no—
691C2×C4—182no—
692C2×C4—182no—
693C2×C4—544no—
694C2×C4C2×#111312yes—
695C2×C4C2×#111311yescharacteristic
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×C3#6431511yescharacteristic
711C2×C3#6431511yescharacteristic
712C2×C3#6431611yescharacteristic
713C2×C3D3×#23911yescharacteristic
714C2×C3D3×#23911yescharacteristic
715C2×C3#6431911yescharacteristic
716C2×C3C2×#380411yescharacteristic
717C2×C3C2×#380411yescharacteristic
718C2×C3C2×#380511yescharacteristic
719D3—62no—
720D3—62no—
721D3—122no—
722D3—122no—
723D3—121no—
724D3—121no—
725C22—92no—
726C22—181no—
727C22—181no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22C22×#111311yescharacteristic
732C4—22no—
733C4—181no—
734C4—182no—
735C4—182no—
736C4—182no—
737C4—181no—
738C4—181no—
739C4—181no—
740C4#8904612yes—
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3#1059534411yescharacteristic, complemented
746C3#1059537911yescharacteristic, complemented
747C3#1059538011yescharacteristic, complemented
748C2—182no—
749C2—361no—
750C2#1172462411yescharacteristic
751C2#1172462611yescharacteristic
752C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radicalC2×#6295C22
hypercenterC2×Q8#1113
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#64155C2semidirect
2. C3×#64155C2semidirect
3. C3×Q8×C3⋊Dic3C2semidirect
6. #11723689C2semidirect
7. #11723683C2semidirect
8. #11723680C2semidirect
9. #11723676C2semidirect
10. #11723669C2semidirect
11. #11723667C2semidirect
38. #64155D3semidirect
39. #64155D3semidirect
40. Q8×C3⋊Dic3D3semidirect
476. C33#552semidirect
677. C32#5581semidirect
678. C32#5639semidirect
679. C32#5642semidirect
745. C3#10595344semidirect
746. C3#10595379semidirect
747. C3#10595380semidirect

Maximal subgroups

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

subgroupindex
C3×#641552
C3×Q8×C3⋊Dic32
C4×#62952
#117236902
#117236892
#117236832
#117236802
#117236762
#117236692
#117236672
#105953803
#105953793
#105953443