Finite Group Databasebeta

← #13168677

Subgroups — #13168677

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6295C211yesmaximal, characteristic
2C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3#11723447C211yesmaximal, characteristic, complemented
4#11723435C211yesmaximal, characteristic, complemented
5C3×#63871C211yesmaximal, characteristic, complemented
6C3×#63849C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723024C212yesmaximal, complemented
9#11723012C212yesmaximal, complemented
10#11722997C212yesmaximal
11#11722919C212yesmaximal, complemented
12#10595379—31nomaximal
13#10594456—31nomaximal
14#10594337—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6295C2211yescharacteristic
19C2×Dic3×C3⋊D3C2212yes—
20C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
21C3×C4×C3⋊Dic3C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24#88815C2211yescharacteristic
25#88814C2211yescharacteristic
26#88814C2211yescharacteristic
27#88807C2212yes—
28#88806C2212yes—
29#88806C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×#3722C2212yes—
36C3×Dic32C2212yes—
37C3×Dic32C2212yes—
38#64155—31no—
39C4⋊C4×C3⋊D3—31no—
40#64099—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#897—31no—
44C3×#892—31no—
45C3×#892—31no—
46C3×#887—31no—
47C4×#626—31no—
48C4×#626—31no—
49C4×#625—31no—
50#63891—32no—
51#63890—32no—
52D3×C4⋊Dic3—31no—
53D3×C4⋊Dic3—31no—
54D3×C4⋊Dic3—61no—
55#63877—32no—
56#63877—32no—
57#63874—32no—
58#63871D311yescharacteristic, complemented
59#63869—31no—
60#63869—31no—
61#63869—32no—
62#63869—61no—
63#63868—32no—
64#63867—32no—
65#63859—32no—
66#63858—32no—
67#63856—31no—
68#63856—31no—
69#63856—61no—
70#63853—32no—
71#63849D311yescharacteristic, complemented
72#63846—32no—
73#63843D311yescharacteristic, complemented
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—22no—
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×Dic6—22no—
88#6295—22no—
89Dic3×C3⋊D3—24no—
90#5642—91no—
91#5581—91no—
92#5529—91no—
93C2×C32×Q8—31no—
94C2×C4×C3⋊D3—32no—
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×C4×C3⋊D3C2×D311yescharacteristic
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—61no—
102C2×C3×C4×D3—61no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2×D311yescharacteristic
105C2×C3×Dic6C2×D311yescharacteristic
106C2×#626—31no—
107C2×#626—31no—
108C2×#625—31no—
109C2×D3×Dic3—32no—
110C2×D3×Dic3—32no—
111C2×D3×Dic3—62no—
112C32×C4⋊C4—31no—
113C32×C4⋊C4—31no—
114#3752—32no—
115C4⋊(C3⋊Dic3)—31no—
116C4⋊(C3⋊Dic3)—31no—
117C4⋊(C3⋊Dic3)—31no—
118C4⋊(C3⋊Dic3)—32no—
119C4⋊(C3⋊Dic3)—61no—
120C4⋊(C3⋊Dic3)—61no—
121C4⋊(C3⋊Dic3)—61no—
122C4⋊(C3⋊Dic3)—121no—
123#3750—32no—
124#3750—32no—
125#3750—32no—
126C4×C3⋊Dic3C2×D311yescharacteristic
127C3×(C2×D3)⋊C4—32no—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—32no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3—32no—
134C3×C4⋊Dic3—32no—
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×C4⋊Dic3C2×D311yescharacteristic
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—32no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—61no—
148#3724—31no—
149#3724—32no—
150#3724—32no—
151#3724—32no—
152#3724—32no—
153#3724—62no—
154#3724—62no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3—62no—
163Dic3⋊Dic3C2×D312yes—
164Dic3⋊Dic3C2×D312yes—
165#3722—31no—
166#3722—31no—
167#3722C2×D312yes—
168#3722C2×D312yes—
169(C2×D3)⋊Dic3—31no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—62no—
176Dic32C2×D312yes—
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×C22⋊Q8—91no—
195C3×C4×Q8—91no—
196C3×#117—91no—
197#946—31no—
198#946—91no—
199#946—91no—
200#946—181no—
201Q8×Dic3—31no—
202C4×#67—91no—
203C4×#67—91no—
204C2×C4⋊Dic3—91no—
205#924—91no—
206#898—92no—
207#897—31no—
208#894—92no—
209#892—31no—
210#892—31no—
211D3×C4⋊C4—91no—
212D3×C4⋊C4—91no—
213D3×C4⋊C4—181no—
214#890—92no—
215#890—91no—
216#890—91no—
217#890—181no—
218#889—92no—
219#887—31no—
220#886—92no—
221#883—92no—
222#879—92no—
223#877—92no—
224#876—92no—
225C4×D12—91no—
226#872—92no—
227#872—92no—
228#870—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—62no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—32no—
243C2×C32×C4—32no—
244C2×C32×C4—32no—
245C2×C32×C4—41no—
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C3⋊Dic3—32no—
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—62no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—122no—
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C4×C3⋊D3—22no—
261C4×C3⋊D3—22no—
262C4×C3⋊D3—64no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D312yes—
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D312yes—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C3×C4×D3—64no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×C4×D3—62no—
288C3×C4×D3—62no—
289C3×C4×D3—122no—
290C3×Dic6—22no—
291C3×Dic6—22no—
292C3×Dic6—42no—
293#626—62no—
294#626—62no—
295#625—62no—
296D3×Dic3—64no—
297D3×Dic3—64no—
298D3×Dic3—124no—
299#552—271noSylow
300C2×C33C2×#4111yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C2×C332−1+411yescharacteristic
303C3×C3⋊D3—22no—
304C3×C3⋊D3—41no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C2×#67—91no—
311C2×#67—91no—
312C22×Dic3—92no—
313C2×D12—91no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—92no—
321C2×C4×D3—92no—
322C2×C4×D3—182no—
323C2×Dic6D3211yescharacteristic
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—92no—
331C3×C4⋊C4—92no—
332C3×C22⋊C4—92no—
333C3×C22⋊C4—92no—
334C3×C42—92no—
335C3×C42—92no—
336C3×C42—91no—
337#217—91no—
338#217—91no—
339#217—92no—
340(C2×D3)⋊C4—32no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—32no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—91no—
345(C2×D3)⋊C4—91no—
346(C2×D3)⋊C4—91no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—182no—
351C4⋊Dic3—32no—
352C4⋊Dic3—32no—
353C4⋊Dic3—91no—
354C4⋊Dic3—92no—
355C4⋊Dic3—92no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—92no—
360C4⋊Dic3—182no—
361C4⋊Dic3—181no—
362C4⋊Dic3—181no—
363C4⋊Dic3—181no—
364C4⋊Dic3—361no—
365C4⋊Dic3D3211yescharacteristic
366C4⋊Dic3D3211yescharacteristic
367Dic3⋊C4—32no—
368Dic3⋊C4—32no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—182no—
381Dic3⋊C4—182no—
382Dic3⋊C4—182no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—32no—
386C4×Dic3—32no—
387C4×Dic3—32no—
388C4×Dic3—32no—
389C4×Dic3—61no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—41no—
394C22×C32C23×D311yescharacteristic
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C2×C3⋊D3—21no—
398C2×C3⋊D3—21no—
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3#23912yes—
403C2×C3×D3—32no—
404C2×C3×D3—32no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
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—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—22no—
424C32×C4—42no—
425C32×C4—62no—
426C32×C4—62no—
427C32×C4—62no—
428C32×C4#23512yes—
429C32×C4#23512yes—
430C32×C4#23712yes—
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
434C3⋊Dic3—21no—
435C3⋊Dic3—62no—
436C3⋊Dic3—62no—
437C3⋊Dic3—62no—
438C3⋊Dic3—122no—
439C3⋊Dic3—122no—
440C3⋊Dic3—122no—
441C3⋊Dic3—242no—
442C3×Dic3—22no—
443C3×Dic3—22no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—42no—
449C3×Dic3—42no—
450C3×Dic3—42no—
451C3×Dic3—62no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—121no—
461C3×Dic3—121no—
462C3×Dic3—121no—
463#126—272no—
464#125—271no—
465#125—272no—
466#123—272no—
467C22⋊Q8—91no—
468C22⋊Q8—271no—
469C4×Q8—91no—
470C4×D4—271no—
471#117—91no—
472#117—272no—
473C2×C4⋊C4—271no—
474C33#55211yescharacteristic, complemented, Sylow
475C23×C3—91no—
476C23×C3—91no—
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—61no—
482C22×D3—61no—
483C3×Q8—62no—
484C3×Q8—62no—
485C3×Q8—122no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—41no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
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—184no—
529C2×Dic3—362no—
530C2×Dic3C2×D3212yes—
531C2×Dic3C2×D3212yes—
532C2×Dic3C2×D3212yes—
533D12—182no—
534C4×D3—64no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—62no—
539C4×D3—122no—
540C4×D3—184no—
541C4×D3—184no—
542C4×D3—364no—
543Dic6—22no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—41no—
554C2×C32—41no—
555C2×C32—41no—
556C2×C32C2×#23511yescharacteristic
557C2×C32C2×#23511yescharacteristic
558C2×C32C2×#23711yescharacteristic
559C2×C32C2×#23911yescharacteristic
560C2×C32#100711yescharacteristic
561C2×C32D3×#4111yescharacteristic
562C2×C32D3×#4111yescharacteristic
563C2×C32#101011yescharacteristic
564C2×C32#101011yescharacteristic
565C3⋊D3—22no—
566C3⋊D3—41no—
567C3×D3—64no—
568C3×D3—62no—
569C3×D3—62no—
570C3×D3—122no—
571C3×D3—121no—
572C3×D3—121no—
573C2×Q8—31no—
574C2×D4—271no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—272no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—92no—
581C4⋊C4—92no—
582C4⋊C4—272no—
583C4⋊C4—272no—
584C4⋊C4—272no—
585C4⋊C4—272no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C22⋊C4—92no—
589C22⋊C4—92no—
590C22⋊C4—272no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C42—92no—
594C42—92no—
595C42—91no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—92no—
601C22×C3—181no—
602C22×C3—181no—
603C22×C3—181no—
604C22×C3—181no—
605C22×C3—181no—
606C22×C3C22×D3211yescharacteristic
607C22×C3C22×D3211yescharacteristic
608C22×C3C22×D3211yescharacteristic
609C2×D3—32no—
610C2×D3—32no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—62no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—121no—
626C2×D3—121no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—42no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—122no—
638C3×C4—122no—
639C3×C4—122no—
640C3×C4—181no—
641C3×C4—181no—
642C3×C4—181no—
643C3×C4—181no—
644C3×C4#379512yes—
645C3×C4#379812yes—
646C3×C4#380412yes—
647Dic3—22no—
648Dic3—22no—
649Dic3—22no—
650Dic3—62no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—61no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—182no—
663Dic3—182no—
664Dic3—182no—
665Dic3—362no—
666Dic3—362no—
667Dic3—362no—
668Dic3—722no—
669C32—21no—
670C32—21no—
671C32—21no—
672C32—41no—
673C32#552911yescharacteristic, complemented
674C32#558111yescharacteristic, complemented
675C32#564211yescharacteristic, complemented
676C23—91no—
677C23—91no—
678Q8—62no—
679D4—542no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—91no—
687C2×C4—182no—
688C2×C4—182no—
689C2×C4—272no—
690C2×C4—544no—
691C2×C4D3311yescharacteristic
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—182no—
705C2×C3—361no—
706C2×C3C2×#379511yescharacteristic
707C2×C3C2×#379811yescharacteristic
708C2×C3#6430911yescharacteristic
709C2×C3#6431211yescharacteristic
710C2×C3#6431511yescharacteristic
711C2×C3#6431511yescharacteristic
712C2×C3D3×#23911yescharacteristic
713C2×C3D3×#23911yescharacteristic
714C2×C3C2×#380411yescharacteristic
715D3—64no—
716D3—62no—
717D3—62no—
718D3—122no—
719D3—121no—
720D3—121no—
721C22—92no—
722C22—181no—
723C22—181no—
724C22—181no—
725C22—181no—
726C22—181no—
727C22C2×D3311yescharacteristic
728C4—62no—
729C4—62no—
730C4—62no—
731C4—181no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—542no—
736C4#8896012yes—
737C3—21no—
738C3—21no—
739C3—21no—
740C3—41no—
741C3#1059433711yescharacteristic, complemented
742C3#1059445611yescharacteristic, complemented
743C3#1059537911yescharacteristic, complemented
744C2—182no—
745C2—361no—
746C2#1172437711yescharacteristic
747C2#1172439411yescharacteristic
748C2C2×#8896011yescharacteristic
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. C3⋊D3×C4⋊Dic3C2semidirect
3. #11723447C2semidirect
4. #11723435C2semidirect
5. C3×#63871C2semidirect
6. C3×#63849C2semidirect
7. C3×#63843C2semidirect
8. #11723024C2semidirect
9. #11723012C2semidirect
11. #11722919C2semidirect
58. #63871D3semidirect
71. #63849D3semidirect
73. #63843D3semidirect
474. C33#552semidirect
673. C32#5529semidirect
674. C32#5581semidirect
675. C32#5642semidirect
741. C3#10594337semidirect
742. C3#10594456semidirect
743. C3#10595379semidirect

Maximal subgroups

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

subgroupindex
C4×#62952
C3⋊D3×C4⋊Dic32
#117234472
#117234352
C3×#638712
C3×#638492
C3×#638432
#117230242
#117230122
#117229972
#117229192
#105953793
#105944563
#105943373