Finite Group Databasebeta

← #13169169

Subgroups — #13169169

Order 1728.

1174 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic, complemented
2#11723536C211yesmaximal, characteristic, complemented
3C4×#6290C211yesmaximal, characteristic
4#11723410C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63857C211yesmaximal, characteristic, complemented
8#11723016C212yesmaximal, complemented
9#11722975C212yesmaximal, complemented
10#11722972C212yesmaximal, complemented
11#11722930C212yesmaximal
12#10594991—31nomaximal
13#10594532—31nomaximal
14#10594531—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6293C2212yes—
19C2×#6290C2211yescharacteristic
20C2×C3×#624C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26#88815C2212yes—
27#88814C2212yes—
28#88807C2212yes—
29#88806C2211yescharacteristic
30#88806C2212yes—
31#88803C2211yescharacteristic
32(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
33Dic3×C3⋊Dic3C2212yes—
34C3×#3724C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C4×#638—31no—
39#64097—31no—
40#64096—31no—
41C2×C3×C4⋊Dic3—31no—
42C3×#924—31no—
43C3×#897—31no—
44C3×D3×C4⋊C4—31no—
45C3×D3×C4⋊C4—31no—
46C3×D3×C4⋊C4—31no—
47#63964—32no—
48#63952—32no—
49#63919—31no—
50#63919—31no—
51#63919—61no—
52C4×#625—31no—
53C4×#625—31no—
54C4×#625—32no—
55C4×#625—61no—
56#63900D311yescharacteristic, complemented
57#63896—32no—
58#63895—32no—
59D3×C4⋊Dic3D311yescharacteristic, complemented
60#63879—32no—
61#63871—31no—
62#63870—32no—
63#63857—31no—
64#63857—32no—
65#63857D311yescharacteristic, complemented
66#63856—31no—
67#63851—32no—
68#63851—32no—
69#63847—32no—
70#63847—32no—
71#63843—31no—
72#63843—31no—
73#63843—61no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—22no—
83C3×#634—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6293—42no—
89#6290Q814yescomplemented
90C3×#624—42no—
91C3×D3×Dic3—42no—
92#5635—91no—
93#5511—91no—
94#5511—91no—
95C22×C32×C4—31no—
96C2×#638—31no—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×#634—32no—
99C2×#634C2×D311yescharacteristic
100C22×C3×Dic3—32no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—61no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—61no—
113C2×#627—32no—
114C2×#627—32no—
115C2×#627—62no—
116C2×#625—31no—
117C2×#625—31no—
118C2×#625—61no—
119C2×#624C2×D312yes—
120C2×D3×Dic3C2×D312yes—
121C32×C4⋊C4—31no—
122C32×C4⋊C4—31no—
123#3757—31no—
124#3752—31no—
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126#3750—32no—
127#3750—32no—
128#3750—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×#217—32no—
138C3×(C2×D3)⋊C4—32no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—32no—
144C3×C4⋊Dic3—32no—
145C3×C4⋊Dic3—61no—
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×Dic3⋊C4—32no—
151C3×Dic3⋊C4—32no—
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—32no—
154#3724—32no—
155#3724—31no—
156#3724—32no—
157#3724—31no—
158#3724—32no—
159#3724—61no—
160#3724—62no—
161#3724C2×D312yes—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—62no—
167Dic3⋊Dic3C2×D312yes—
168Dic3⋊Dic3C2×D312yes—
169#3722—32no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—61no—
177(C2×D3)⋊Dic3—61no—
178(C2×D3)⋊Dic3C2×D312yes—
179Dic32—32no—
180Dic32—32no—
181Dic32—62no—
182C22×C33C2411yescharacteristic
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3C2×Q812yes—
186C2×C32×D3—21no—
187C2×C32×D3—21no—
188C2×C32×D3C2×Q812yes—
189C33×C4#4112yes—
190C3⋊(C3⋊Dic3)—21no—
191C3⋊(C3⋊Dic3)C2×Q812yes—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—22no—
195C32×Dic3—21no—
196C32×Dic3—22no—
197C32×Dic3—22no—
198C3×C22⋊Q8—91no—
199C2×C3×C4⋊C4—91no—
200C2×C3×C4⋊C4—91no—
201#946—91no—
202Q8×Dic3—91no—
203C4×#67—92no—
204C4×#67—92no—
205C4×#67—91no—
206C4×#67—91no—
207C4×#67—91no—
208C4×#67—181no—
209C2×C4⋊Dic3—31no—
210#924—31no—
211#924—92no—
212#924—92no—
213#924—91no—
214#897—31no—
215#897—92no—
216#897—91no—
217#896—92no—
218#896—92no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—31no—
221D3×C4⋊C4—31no—
222#889—92no—
223#889—92no—
224#889—92no—
225#888—91no—
226#888—91no—
227#888—91no—
228#888—181no—
229#887—91no—
230#887—91no—
231#887—181no—
232#67⋊C4—92no—
233#878—92no—
234C23×C32—31no—
235C22×C3⋊D3C22×D311yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—31no—
238C22×C3×D3—31no—
239C22×C3×D3—61no—
240C22×C3×D3C22×D311yescharacteristic
241C22×C3×D3C22×D311yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—31no—
246C2×C32×C4—32no—
247C2×C32×C4—32no—
248C2×C32×C4—41no—
249C2×C32×C4—62no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253#638—34no—
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×D312yes—
269C2×C3⋊Dic3C22×D312yes—
270C2×C3⋊Dic3C22×D311yescharacteristic
271C4×C3⋊D3—22no—
272#634—22no—
273#634—122no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—122no—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C3×C4×D3—22no—
294C3×C4×D3—22no—
295C3×C4×D3—42no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×C4×D3—122no—
299C3×C4×D3—122no—
300C3×C4×D3—122no—
301C3×C4×D3—122no—
302C3×Dic6—64no—
303C3×Dic6—62no—
304C3×Dic6—62no—
305#627—122no—
306#627—122no—
307#627—124no—
308#625—34no—
309#625—34no—
310#625—64no—
311#624—42no—
312D3×Dic3—42no—
313#554—271noSylow
314C2×C33C22×Q811yescharacteristic
315C2×C33C2×#4111yescharacteristic
316C2×C33H(5,𝔽2)11yescharacteristic
317C3×C3⋊D3—22no—
318C32×D3—22no—
319C2×C3×Q8—91no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C22×C3×C4—92no—
324C22×C3×C4—92no—
325C22×C3×C4—91no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—181no—
330C22×Dic3—32no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—32no—
334C2×C4×D3—32no—
335C2×C4×D3—32no—
336C2×C4×D3—61no—
337C2×C4×D3D3211yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6—92no—
342C2×Dic6—92no—
343C2×Dic6—92no—
344C2×Dic6—182no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4—92no—
354C3×C4⋊C4—91no—
355C3×C22⋊C4—92no—
356#217—32no—
357#217—92no—
358#217—91no—
359#217—91no—
360#217—91no—
361#217—181no—
362(C2×D3)⋊C4—32no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—181no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—32no—
372C4⋊Dic3—32no—
373C4⋊Dic3—61no—
374C4⋊Dic3—92no—
375C4⋊Dic3—92no—
376C4⋊Dic3D3211yescharacteristic
377C4⋊Dic3D3211yescharacteristic
378Dic3⋊C4—32no—
379Dic3⋊C4—32no—
380Dic3⋊C4—32no—
381Dic3⋊C4—32no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—92no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—92no—
391Dic3⋊C4—91no—
392Dic3⋊C4—182no—
393Dic3⋊C4—182no—
394Dic3⋊C4—181no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—92no—
401C4×Dic3—182no—
402C4×Dic3—181no—
403C4×Dic3—181no—
404C4×Dic3—181no—
405C4×Dic3—361no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—32no—
410C22×C32—41no—
411C22×C32—61no—
412C22×C32—61no—
413C22×C32C23×D311yescharacteristic
414C22×C32C23×D311yescharacteristic
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3D3×Q812yes—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—32no—
425C2×C3×D3—32no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—62no—
429C2×C3×D3—61no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—121no—
434C2×C3×D3—121no—
435C2×C3×D3D3×Q812yes—
436C2×C3×D3D3×Q812yes—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—42no—
441C32×C4—61no—
442C32×C4—62no—
443C32×C4—62no—
444C32×C4#23512yes—
445C32×C4#23512yes—
446C32×C4#23712yes—
447C3⋊Dic3—22no—
448C3⋊Dic3—21no—
449C3⋊Dic3—22no—
450C3⋊Dic3—32no—
451C3⋊Dic3—32no—
452C3⋊Dic3—32no—
453C3⋊Dic3—62no—
454C3⋊Dic3—62no—
455C3⋊Dic3—62no—
456C3⋊Dic3—61no—
457C3⋊Dic3—62no—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—122no—
461C3⋊Dic3—121no—
462C3⋊Dic3—121no—
463C3⋊Dic3—122no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—42no—
471C3×Dic3—41no—
472C3×Dic3—42no—
473C3×Dic3—64no—
474C3×Dic3—62no—
475C3×Dic3—62no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C3×Dic3—62no—
479C3×Dic3—62no—
480C3×Dic3—122no—
481C3×Dic3—121no—
482C4⋊Q8—271no—
483#125—272no—
484C22⋊Q8—91no—
485C22⋊Q8—272no—
486C22⋊Q8—272no—
487C22⋊Q8—271no—
488C4×Q8—271no—
489C4×D4—272no—
490C4×D4—271no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C33#55411yescharacteristic, complemented, Sylow
494C23×C3—31no—
495C23×C3—31no—
496C23×C3—61no—
497C23×C3—91no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3C2×D3211yescharacteristic
502C3×Q8—182no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—31no—
509C2×C3×C4—32no—
510C2×C3×C4—31no—
511C2×C3×C4—32no—
512C2×C3×C4—41no—
513C2×C3×C4—62no—
514C2×C3×C4—61no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—92no—
519C2×C3×C4—91no—
520C2×C3×C4—92no—
521C2×C3×C4—122no—
522C2×C3×C4—182no—
523C2×C3×C4—362no—
524C2×C3×C4—362no—
525C2×C3×C4C2×D3211yescharacteristic
526C2×C3×C4C2×D3211yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528#67—94no—
529#67—94no—
530#67—94no—
531#67—184no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—61no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—122no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—181no—
552C2×Dic3—181no—
553C2×Dic3—181no—
554C2×Dic3—361no—
555C2×Dic3—361no—
556C2×Dic3C2×D3212yes—
557C2×Dic3C2×D3211yescharacteristic
558C2×Dic3C2×D3212yes—
559C4×D3—22no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—122no—
566Dic6—64no—
567Dic6—62no—
568Dic6—62no—
569Dic6—362no—
570Dic6—362no—
571Dic6—362no—
572Dic6—364no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—62no—
586C2×C32C2×#23511yescharacteristic
587C2×C32C2×#23511yescharacteristic
588C2×C32C2×#23711yescharacteristic
589C2×C32#100411yescharacteristic
590C2×C32#100411yescharacteristic
591C2×C32C2×D3×Q811yescharacteristic
592C2×C32C2×D3×Q811yescharacteristic
593C2×C32C2×D3×Q811yescharacteristic
594C2×C32#100911yescharacteristic
595C3⋊D3—22no—
596C3×D3—22no—
597C3×D3—22no—
598C3×D3—42no—
599C3×D3—62no—
600C3×D3—62no—
601C3×D3—122no—
602C2×Q8—91no—
603C2×Q8—272no—
604C2×D4—271no—
605C22×C4—31no—
606C22×C4—92no—
607C22×C4—92no—
608C22×C4—91no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—92no—
612C4⋊C4—92no—
613C4⋊C4—92no—
614C4⋊C4—91no—
615C4⋊C4—271no—
616C4⋊C4—272no—
617C4⋊C4—272no—
618C4⋊C4—272no—
619C22⋊C4—92no—
620C22⋊C4—271no—
621C22⋊C4—272no—
622C22⋊C4—271no—
623C42—272no—
624C42—271no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—32no—
630C22×C3—41no—
631C22×C3—62no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—92no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3C22×D3211yescharacteristic
642C22×C3C22×D3211yescharacteristic
643C22×C3C22×D3211yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—32no—
647C2×D3—32no—
648C2×D3—62no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3#379712yes—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—42no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—122no—
667C3×C4—121no—
668C3×C4—122no—
669C3×C4—182no—
670C3×C4—182no—
671C3×C4—181no—
672C3×C4#379512yes—
673C3×C4#379812yes—
674C3×C4#380412yes—
675Dic3—22no—
676Dic3—22no—
677Dic3—21no—
678Dic3—64no—
679Dic3—62no—
680Dic3—61no—
681Dic3—61no—
682Dic3—62no—
683Dic3—62no—
684Dic3—62no—
685Dic3—92no—
686Dic3—92no—
687Dic3—92no—
688Dic3—122no—
689Dic3—121no—
690Dic3—182no—
691Dic3—182no—
692Dic3—182no—
693Dic3—182no—
694Dic3—181no—
695Dic3—181no—
696Dic3—181no—
697Dic3—362no—
698Dic3—361no—
699Dic3—361no—
700Dic3—362no—
701C32—21no—
702C32—21no—
703C32—21no—
704C32—41no—
705C32#551111yescharacteristic, complemented
706C32#551111yescharacteristic, complemented
707C32#563511yescharacteristic, complemented
708C23—31no—
709C23—91no—
710Q8—182no—
711Q8—1082no—
712D4—274no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—31no—
716C2×C4—62no—
717C2×C4—92no—
718C2×C4—91no—
719C2×C4—92no—
720C2×C4—182no—
721C2×C4—271no—
722C2×C4—271no—
723C2×C4—362no—
724C2×C4—362no—
725C2×C4D3311yescharacteristic
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—62no—
739C2×C3—62no—
740C2×C3—122no—
741C2×C3—182no—
742C2×C3C2×#379511yescharacteristic
743C2×C3C2×#379711yescharacteristic
744C2×C3C2×#379811yescharacteristic
745C2×C3#6430711yescharacteristic
746C2×C3#6431311yescharacteristic
747C2×C3#6431411yescharacteristic
748C2×C3D32×Q811yescharacteristic
749C2×C3D32×Q811yescharacteristic
750C2×C3C2×#380411yescharacteristic
751D3—22no—
752D3—62no—
753D3—62no—
754D3—122no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—92no—
759C22—181no—
760C22—181no—
761C22C2×D3311yescharacteristic
762C4—62no—
763C4—62no—
764C4—61no—
765C4—182no—
766C4—181no—
767C4—182no—
768C4—272no—
769C4—541no—
770C4#8896012yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059453111yescharacteristic, complemented
776C3#1059453211yescharacteristic, complemented
777C3#1059499111yescharacteristic, complemented
778C2—62no—
779C2—182no—
780C2D3×#379711yescharacteristic
781C2#1172438111yescharacteristic
782C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6290C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723674C2semidirect
2. #11723536C2semidirect
4. #11723410C2semidirect
5. C3×#63900C2semidirect
6. C3×D3×C4⋊Dic3C2semidirect
7. C3×#63857C2semidirect
8. #11723016C2semidirect
9. #11722975C2semidirect
10. #11722972C2semidirect
56. #63900D3semidirect
59. D3×C4⋊Dic3D3semidirect
65. #63857D3semidirect
89. #6290Q8semidirect
493. C33#554semidirect
705. C32#5511semidirect
706. C32#5511semidirect
707. C32#5635semidirect
775. C3#10594531semidirect
776. C3#10594532semidirect
777. C3#10594991semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117235362
C4×#62902
#117234102
C3×#639002
C3×D3×C4⋊Dic32
C3×#638572
#117230162
#117229752
#117229722
#117229302
#105949913
#105945323
#105945313