Finite Group Databasebeta

← #13168733

Subgroups — #13168733

Order 1728.

1168 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#11723689C211yesmaximal, characteristic, complemented
2#11723431C211yesmaximal, characteristic, complemented
3#11723426C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic
7C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#11723013C212yesmaximal, complemented
9#11722979C212yesmaximal, complemented
10#11722969C212yesmaximal, complemented
11#11722927C212yesmaximal
12#10594988—31nomaximal
13#10594537—31nomaximal
14#10593956—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6294C2212yes—
19C2×C3×#627C2212yes—
20C2×C3×#626C2211yescharacteristic
21C2×C3×D3×Dic3C2212yes—
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4×Dic3C2211yescharacteristic
26#88815C2212yes—
27#88807C2212yes—
28#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30#88803C2212yes—
31(C2×D3)⋊(C3⋊Dic3)C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38#64133—31no—
39#64106—31no—
40C4×#634—31no—
41C3×C4×#67—31no—
42C2×C3×C4⋊Dic3—31no—
43C3×D3×C4⋊C4—31no—
44C3×#888—31no—
45C3×C4×D12—31no—
46C3×#869—31no—
47Dic3×#67—32no—
48#63964—32no—
49#63918D311yescharacteristic, complemented
50#63904—32no—
51C4×#626D311yescharacteristic
52#63900—31no—
53#63899—32no—
54#63898—32no—
55D3×C4⋊Dic3—31no—
56D3×C4⋊Dic3—31no—
57D3×C4⋊Dic3D311yescharacteristic, complemented
58#63888—32no—
59#63887—32no—
60#63887—32no—
61#63872—32no—
62#63857—31no—
63#63857—31no—
64#63857—31no—
65#63857—31no—
66#63857—61no—
67#63857—61no—
68#63856—32no—
69#63846—32no—
70#63845—32no—
71#63844—31no—
72#63844—31no—
73#63844—61no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308—22no—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88#6294—42no—
89C3×#627—42no—
90C3×#626Q814yescomplemented
91C3×D3×Dic3—42no—
92#5730—91no—
93#5543—91no—
94#5511—91no—
95C22×C32×C4—31no—
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×#67—31no—
105C22×C3×Dic3—32no—
106C2×C3×D12—31no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—31no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C2×D311yescharacteristic
114C2×C3×Dic6—32no—
115C2×C3×Dic6—32no—
116C2×#627C2×D312yes—
117C2×#626C2×D311yescharacteristic
118C2×#624—32no—
119C2×D3×Dic3—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3C2×D312yes—
122C32×C4⋊C4—31no—
123C32×C42—31no—
124#3757—32no—
125#3752—32no—
126C4⋊(C3⋊Dic3)—32no—
127C4⋊(C3⋊Dic3)C2×D311yescharacteristic
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic
129#3750—32no—
130#3750—32no—
131C4×C3⋊Dic3—32no—
132C3×#217—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—32no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3—61no—
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×Dic3⋊C4—31no—
151C3×C4×Dic3—21no—
152C3×C4×Dic3C2×D311yescharacteristic
153C3×C4×Dic3C2×D311yescharacteristic
154#3724—32no—
155#3724—32no—
156#3724—32no—
157#3724—62no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—62no—
165Dic3⋊Dic3—62no—
166Dic3⋊Dic3C2×D311yescharacteristic
167Dic3⋊Dic3C2×D312yes—
168Dic3⋊Dic3C2×D312yes—
169#3722C2×D311yescharacteristic
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—62no—
175(C2×D3)⋊Dic3—62no—
176(C2×D3)⋊Dic3C2×D311yescharacteristic
177Dic32—32no—
178Dic32—32no—
179Dic32—62no—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3C2×Q812yes—
184C2×C32×D3—21no—
185C2×C32×D3—21no—
186C2×C32×D3C2×Q812yes—
187C33×C4#4112yes—
188C3⋊(C3⋊Dic3)—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—22no—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—21no—
195C32×Dic3C2×Q812yes—
196C3×C4⋊Q8—91no—
197C3×C4×D4—91no—
198C2×C3×C4⋊C4—91no—
199#946—92no—
200#946—92no—
201D4×Dic3—92no—
202C4×#67—31no—
203C4×#67—92no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—91no—
206#924—91no—
207#924—91no—
208#924—92no—
209#924—91no—
210#924—181no—
211#897—91no—
212#897—91no—
213#897—91no—
214#897—181no—
215#896—92no—
216#893—92no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—91no—
219D3×C4⋊C4—91no—
220#890—92no—
221#890—92no—
222#889—92no—
223#888—31no—
224#887—91no—
225#878—92no—
226#878—92no—
227C4×D12—31no—
228#869—31no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—181no—
232C23×C32—31no—
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—21no—
235C22×C3×D3—31no—
236C22×C3×D3—31no—
237C22×C3×D3—61no—
238C22×C3×D3C22×D311yescharacteristic
239C22×C3×D3C22×D311yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—31no—
244C2×C32×C4—32no—
245C2×C32×C4—31no—
246C2×C32×C4—31no—
247C2×C32×C4—41no—
248C2×C32×C4—62no—
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—
261C2×C3⋊Dic3C22×D312yes—
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—
270C3×#67—34no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—122no—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C3×D12—34no—
294C3×C4×D3—22no—
295C3×C4×D3—22no—
296C3×C4×D3—42no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3—122no—
300C3×C4×D3—122no—
301C3×Dic6—122no—
302C3×Dic6—122no—
303#627—42no—
304#626Dic614yescomplemented
305#624—122no—
306D3×Dic3—42no—
307D3×Dic3—122no—
308D3×Dic3—122no—
309#554—271noSylow
310C2×C33C22×Q811yescharacteristic
311C2×C33C2×#4111yescharacteristic
312C2×C33H(5,𝔽2)11yescharacteristic
313C3×C3⋊D3—22no—
314C32×D3—22no—
315C2×C3×Q8—92no—
316C2×C3×D4—91no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×C3×C4—92no—
321C22×C3×C4—91no—
322C2×#67—31no—
323C22×Dic3—32no—
324C22×Dic3—92no—
325C2×D12—31no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—32no—
329C2×C4×D3—61no—
330C2×C4×D3—92no—
331C2×C4×D3—92no—
332C2×C4×D3D3211yescharacteristic
333C2×Dic6—32no—
334C2×Dic6—32no—
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—91no—
347C3×C4⋊C4—92no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C42—31no—
353C3×C42—31no—
354C3×C42—61no—
355#217—31no—
356#217—92no—
357#217—92no—
358#217—92no—
359#217—182no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—182no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—32no—
372C4⋊Dic3—31no—
373C4⋊Dic3—32no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—92no—
377C4⋊Dic3—92no—
378C4⋊Dic3—92no—
379C4⋊Dic3—92no—
380C4⋊Dic3—182no—
381C4⋊Dic3D3211yescharacteristic
382Dic3⋊C4—32no—
383Dic3⋊C4—31no—
384Dic3⋊C4—32no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391Dic3⋊C4—92no—
392Dic3⋊C4—92no—
393Dic3⋊C4—182no—
394Dic3⋊C4—182no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—92no—
398C4×Dic3—182no—
399C4×Dic3D3211yescharacteristic
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—32no—
404C22×C32—41no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D311yescharacteristic
408C22×C32C23×D311yescharacteristic
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3C2×Dic612yes—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—32no—
419C2×C3×D3—32no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—62no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—121no—
428C2×C3×D3—121no—
429C2×C3×D3C2×Dic612yes—
430C2×C3×D3D3×Q812yes—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—32no—
435C32×C4—42no—
436C32×C4—61no—
437C32×C4—61no—
438C32×C4—62no—
439C32×C4#23512yes—
440C32×C4#23712yes—
441C32×C4#23912yes—
442C3⋊Dic3—21no—
443C3⋊Dic3—22no—
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—22no—
455C3×Dic3—21no—
456C3×Dic3—22no—
457C3×Dic3—21no—
458C3×Dic3—22no—
459C3×Dic3—41no—
460C3×Dic3—41no—
461C3×Dic3—42no—
462C3×Dic3—61no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—61no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—121no—
469C3×Dic3—122no—
470C3×Dic3—122no—
471C3×Dic3C2×Dic612yes—
472C3×Dic3D3×Q812yes—
473C4⋊Q8—91no—
474#125—272no—
475C22⋊Q8—272no—
476C22⋊Q8—272no—
477C22⋊Q8—271no—
478C22⋊Q8—271no—
479C4×Q8—271no—
480C4×D4—91no—
481C4×D4—272no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—271no—
484C33#55411yescharacteristic, complemented, Sylow
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—91no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—61no—
492C22×D3C2×D3211yescharacteristic
493C3×Q8—362no—
494C3×D4—94no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—92no—
514C2×C3×C4—91no—
515C2×C3×C4—92no—
516C2×C3×C4—122no—
517C2×C3×C4—182no—
518C2×C3×C4—362no—
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522#67—34no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—32no—
529C2×Dic3—62no—
530C2×Dic3—62no—
531C2×Dic3—61no—
532C2×Dic3—92no—
533C2×Dic3—92no—
534C2×Dic3—92no—
535C2×Dic3—122no—
536C2×Dic3—182no—
537C2×Dic3—182no—
538C2×Dic3—182no—
539C2×Dic3—362no—
540C2×Dic3—362no—
541C2×Dic3C2×D3211yescharacteristic
542C2×Dic3C2×D3211yescharacteristic
543C2×Dic3C2×D3212yes—
544C2×Dic3C2×D3211yescharacteristic
545D12—34no—
546C4×D3—22no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—362no—
552C4×D3—362no—
553Dic6—122no—
554Dic6—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×C32—62no—
575C2×C32C22×Dic611yescharacteristic
576C2×C32C2×#23511yescharacteristic
577C2×C32C2×#23711yescharacteristic
578C2×C32#100411yescharacteristic
579C2×C32#100411yescharacteristic
580C2×C32C2×D3×Q811yescharacteristic
581C2×C32C2×D3×Q811yescharacteristic
582C2×C32C2×#23911yescharacteristic
583C2×C32#100911yescharacteristic
584C3⋊D3—22no—
585C3×D3—22no—
586C3×D3—22no—
587C3×D3—42no—
588C3×D3—62no—
589C3×D3—62no—
590C3×D3—122no—
591C2×Q8—92no—
592C2×Q8—271no—
593C2×D4—91no—
594C22×C4—31no—
595C22×C4—92no—
596C22×C4—91no—
597C22×C4—272no—
598C4⋊C4—31no—
599C4⋊C4—92no—
600C4⋊C4—91no—
601C4⋊C4—92no—
602C4⋊C4—91no—
603C4⋊C4—91no—
604C4⋊C4—272no—
605C4⋊C4—272no—
606C4⋊C4—272no—
607C4⋊C4—272no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—272no—
611C22⋊C4—272no—
612C42—31no—
613C42—272no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—32no—
618C22×C3—32no—
619C22×C3—41no—
620C22×C3—62no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—92no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3C22×D3211yescharacteristic
631C22×C3C22×D3211yescharacteristic
632C22×C3C22×D3211yescharacteristic
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—32no—
636C2×D3—32no—
637C2×D3—62no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3D3×Dic612yes—
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—61no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—121no—
659C3×C4—122no—
660C3×C4—121no—
661C3×C4—181no—
662C3×C4—182no—
663C3×C4—182no—
664C3×C4#379612yes—
665C3×C4#379912yes—
666C3×C4#380412yes—
667Dic3—21no—
668Dic3—22no—
669Dic3—21no—
670Dic3—61no—
671Dic3—62no—
672Dic3—62no—
673Dic3—62no—
674Dic3—62no—
675Dic3—61no—
676Dic3—121no—
677Dic3—122no—
678Dic3—122no—
679Dic3—184no—
680Dic3—182no—
681Dic3—182no—
682Dic3—182no—
683Dic3—362no—
684Dic3—362no—
685Dic3—364no—
686Dic3D3×Dic612yes—
687C32—21no—
688C32—21no—
689C32—21no—
690C32—41no—
691C32#551111yescharacteristic, complemented
692C32#554311yescharacteristic, complemented
693C32#573011yescharacteristic, complemented
694C23—31no—
695C23—91no—
696Q8—362no—
697Q8—542no—
698D4—94no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—32no—
703C2×C4—62no—
704C2×C4—92no—
705C2×C4—91no—
706C2×C4—92no—
707C2×C4—182no—
708C2×C4—272no—
709C2×C4—362no—
710C2×C4—1082no—
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—62no—
725C2×C3—62no—
726C2×C3—122no—
727C2×C3—182no—
728C2×C3C2×D3×Dic611yescharacteristic
729C2×C3C2×D3×Dic611yescharacteristic
730C2×C3C2×#379611yescharacteristic
731C2×C3C2×#379911yescharacteristic
732C2×C3#6430711yescharacteristic
733C2×C3#6430711yescharacteristic
734C2×C3#6431311yescharacteristic
735C2×C3D32×Q811yescharacteristic
736C2×C3C2×#380411yescharacteristic
737D3—22no—
738D3—62no—
739D3—62no—
740D3—122no—
741C22—32no—
742C22—61no—
743C22—61no—
744C22—92no—
745C22—181no—
746C22—181no—
747C22C2×D3311yescharacteristic
748C4—32no—
749C4—62no—
750C4—61no—
751C4—61no—
752C4—182no—
753C4—182no—
754C4—181no—
755C4—542no—
756C4#8896212yes—
757C3—21no—
758C3—21no—
759C3—21no—
760C3—41no—
761C3#1059395611yescharacteristic, complemented
762C3#1059453711yescharacteristic, complemented
763C3#1059498811yescharacteristic, complemented
764C2—62no—
765C2—182no—
766C2D32×Dic611yescharacteristic
767C2#1172438011yescharacteristic
768C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
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. #11723689C2semidirect
2. #11723431C2semidirect
3. #11723426C2semidirect
4. #11723399C2semidirect
5. C3×#63918C2semidirect
7. C3×D3×C4⋊Dic3C2semidirect
8. #11723013C2semidirect
9. #11722979C2semidirect
10. #11722969C2semidirect
49. #63918D3semidirect
57. D3×C4⋊Dic3D3semidirect
90. C3×#626Q8semidirect
304. #626Dic6semidirect
484. C33#554semidirect
691. C32#5511semidirect
692. C32#5543semidirect
693. C32#5730semidirect
761. C3#10593956semidirect
762. C3#10594537semidirect
763. C3#10594988semidirect

Maximal subgroups

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

subgroupindex
#117236892
#117234312
#117234262
#117233992
C3×#639182
C3×C4×#6262
C3×D3×C4⋊Dic32
#117230132
#117229792
#117229692
#117229272
#105949883
#105945373
#105939563