Finite Group Databasebeta

← #13169303

Subgroups — #13169303

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6294C211yesmaximal, characteristic, complemented
2#11723526C211yesmaximal, characteristic
3#11723494C211yesmaximal, characteristic, complemented
4#11723440C211yesmaximal, characteristic, complemented
5C3×#63872C211yesmaximal, characteristic, complemented
6C3×#63871C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11723028C212yesmaximal, complemented
9#11722999C212yesmaximal, complemented
10#11722937C212yesmaximal, complemented
11#11722920C212yesmaximal, complemented
12#10595376—31nomaximal
13#10594464—31nomaximal
14#10594453—31nomaximal
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×#6292C2212yes—
21C2×#6289C2212yes—
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26#88813C2211yescharacteristic
27#88813C2211yescharacteristic
28#88804C2212yes—
29#88804C2212yes—
30#88804C2212yes—
31#88804C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38#64156—31no—
39#64104—31no—
40#64102—31no—
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#897—31no—
44C3×#890—31no—
45C3×#890—31no—
46C3×#887—31no—
47#63909—31no—
48#63909—31no—
49#63909—61no—
50#63897—32no—
51#63894—31no—
52#63894—31no—
53#63894—32no—
54#63894—61no—
55#63890—32no—
56#63890—32no—
57C4×#624—31no—
58#63881—32no—
59#63880—32no—
60C4×D3×Dic3—31no—
61C4×D3×Dic3—31no—
62#63872D311yescharacteristic, complemented
63#63871D311yescharacteristic, complemented
64#63864—31no—
65#63864—31no—
66#63864—61no—
67#63849—32no—
68#63848—32no—
69#63848—32no—
70#63848—32no—
71#63843D311yescharacteristic, complemented
72#63836—32no—
73#63836—32no—
74C22×C3⋊(C3⋊D3)C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C4⋊(C3⋊(C3⋊D3))—22no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×Dic6—22no—
88#6294—22no—
89#6294—22no—
90#6292—24no—
91#6289—24no—
92#5691—91no—
93#5624—91no—
94#5580—91no—
95C2×C32×Q8—31no—
96C2×C4⋊(C3⋊D3)—32no—
97C2×C4⋊(C3⋊D3)—31no—
98C2×C4⋊(C3⋊D3)—31no—
99C2×C4⋊(C3⋊D3)—31no—
100C2×C4⋊(C3⋊D3)—61no—
101C2×C4⋊(C3⋊D3)—61no—
102C2×C4⋊(C3⋊D3)—61no—
103C2×C4⋊(C3⋊D3)—121no—
104C2×C4×C3⋊D3—32no—
105C2×C4×C3⋊D3C2×D311yescharacteristic
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—61no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C2×D311yescharacteristic
112C2×#626—32no—
113C2×#626—32no—
114C2×#626—62no—
115C2×#624—31no—
116C2×#624—31no—
117C2×#624—32no—
118C2×#624—32no—
119C2×#624—62no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C2×D3×Dic3—31no—
124C32×C4⋊C4—31no—
125C32×C4⋊C4—31no—
126#3752—32no—
127#3752—32no—
128#3752—32no—
129#3752—32no—
130C4×C3⋊Dic3C2×D311yescharacteristic
131C4×C3⋊Dic3C2×D311yescharacteristic
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—32no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—61no—
155C3×C4×Dic3—61no—
156Dic3⋊Dic3C2×D312yes—
157Dic3⋊Dic3C2×D312yes—
158Dic3⋊Dic3C2×D312yes—
159Dic3⋊Dic3C2×D312yes—
160#3722—32no—
161#3722—32no—
162#3722—32no—
163#3722—32no—
164#3722—32no—
165#3722—32no—
166#3722—32no—
167#3722—32no—
168#3722—62no—
169#3722—62no—
170#3722—62no—
171#3722—62no—
172#3722C2×D312yes—
173Dic32—31no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32C2×D312yes—
180C22×C33C2411yescharacteristic
181C2×C3⋊(C3⋊D3)—22no—
182C2×C3⋊(C3⋊D3)—22no—
183C2×C3⋊(C3⋊D3)—22no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4#4112yes—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3#4112yes—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C32×Dic3—22no—
196C3×#125—91no—
197C3×C22⋊Q8—91no—
198C3×C4×Q8—91no—
199#947—91no—
200#947—91no—
201#947—181no—
202#946—31no—
203Q8×Dic3—31no—
204#930—91no—
205C2×C4×Dic3—91no—
206#898—92no—
207#898—92no—
208#898—92no—
209#897—31no—
210#895—91no—
211#895—91no—
212#895—181no—
213#894—92no—
214#894—92no—
215#893—92no—
216#893—91no—
217#893—91no—
218#893—181no—
219#892—92no—
220#892—92no—
221#890—31no—
222#890—31no—
223#887—31no—
224#886—92no—
225#67⋊C4—92no—
226#875—91no—
227C4×D12—92no—
228C4×D12—91no—
229#872—92no—
230C42×D3—91no—
231C42×D3—91no—
232C22×C3⋊D3—32no—
233C22×C3⋊D3—32no—
234C22×C3⋊D3—32no—
235C22×C3⋊D3—62no—
236C22×C3⋊D3—62no—
237C22×C3⋊D3—62no—
238C22×C3⋊D3—122no—
239C22×C3⋊D3C22×D311yescharacteristic
240C22×C3×D3—31no—
241C22×C3×D3—31no—
242C22×C3×D3—61no—
243C32×Q8—62no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—32no—
248C2×C32×C4—32no—
249C2×C32×C4—32no—
250C2×C32×C4—41no—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D311yescharacteristic
259C4⋊(C3⋊D3)—62no—
260C4⋊(C3⋊D3)—64no—
261C4⋊(C3⋊D3)—64no—
262C4⋊(C3⋊D3)—62no—
263C4⋊(C3⋊D3)—62no—
264C4⋊(C3⋊D3)—122no—
265C4⋊(C3⋊D3)—122no—
266C4⋊(C3⋊D3)—124no—
267C4×C3⋊D3—22no—
268C4×C3⋊D3—64no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C3×C4×D3—62no—
294C3×C4×D3—62no—
295C3×C4×D3—122no—
296C3×Dic6—22no—
297C3×Dic6—22no—
298C3×Dic6—42no—
299#626—64no—
300#626—64no—
301#626—124no—
302#624—64no—
303#624—64no—
304#624—62no—
305#624—62no—
306#624—124no—
307D3×Dic3—62no—
308D3×Dic3—62no—
309D3×Dic3—62no—
310D3×Dic3—62no—
311#529—271noSylow
312C2×C33C2×#4111yescharacteristic
313C2×C33C2×#4111yescharacteristic
314C2×C33C2×#4111yescharacteristic
315C3⋊(C3⋊D3)—42no—
316C3×C3⋊D3—22no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C22×C3×C4—91no—
321C2×#67—92no—
322C22×Dic3—91no—
323C22×Dic3—91no—
324C2×D12—92no—
325C2×D12—92no—
326C2×D12—91no—
327C2×D12—91no—
328C2×D12—91no—
329C2×D12—181no—
330C2×D12—181no—
331C2×D12—181no—
332C2×D12—182no—
333C2×D12—361no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—92no—
338C2×C4×D3—92no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—92no—
344C2×C4×D3—182no—
345C2×Dic6D3211yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4—92no—
354C3×C4⋊C4—92no—
355C3×C4⋊C4—92no—
356C3×C22⋊C4—92no—
357C3×C42—92no—
358C3×C42—91no—
359C3×C42—91no—
360(C2×D3)⋊C4—32no—
361(C2×D3)⋊C4—32no—
362(C2×D3)⋊C4—92no—
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—92no—
372(C2×D3)⋊C4—92no—
373(C2×D3)⋊C4—92no—
374(C2×D3)⋊C4—182no—
375(C2×D3)⋊C4—182no—
376(C2×D3)⋊C4—182no—
377(C2×D3)⋊C4—182no—
378C4⋊Dic3—32no—
379C4⋊Dic3—32no—
380C4⋊Dic3—32no—
381C4⋊Dic3—32no—
382C4⋊Dic3D3211yescharacteristic
383C4⋊Dic3D3211yescharacteristic
384Dic3⋊C4—32no—
385Dic3⋊C4—32no—
386Dic3⋊C4—32no—
387Dic3⋊C4—32no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—32no—
393C4×Dic3—32no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32C23×D311yescharacteristic
407C22×C32C23×D311yescharacteristic
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—62no—
412C2×C3⋊D3—64no—
413C2×C3⋊D3—62no—
414C2×C3⋊D3—62no—
415C2×C3⋊D3—62no—
416C2×C3⋊D3—62no—
417C2×C3⋊D3—62no—
418C2×C3⋊D3—62no—
419C2×C3⋊D3—62no—
420C2×C3⋊D3—62no—
421C2×C3⋊D3—122no—
422C2×C3⋊D3—122no—
423C2×C3⋊D3—124no—
424C2×C3⋊D3—122no—
425C2×C3⋊D3—122no—
426C2×C3⋊D3—122no—
427C2×C3⋊D3—122no—
428C2×C3⋊D3—122no—
429C2×C3⋊D3—122no—
430C2×C3⋊D3—242no—
431C2×C3⋊D3—242no—
432C2×C3⋊D3#23912yes—
433C2×C3×D3—32no—
434C2×C3×D3—32no—
435C2×C3×D3—62no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—121no—
441C2×C3×D3—121no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—22no—
445C32×C4—42no—
446C32×C4—62no—
447C32×C4—62no—
448C32×C4—62no—
449C32×C4#23512yes—
450C32×C4#23712yes—
451C32×C4#23912yes—
452C3⋊Dic3—21no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3#23912yes—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—32no—
464C3×Dic3—32no—
465C3×Dic3—42no—
466C3×Dic3—42no—
467C3×Dic3—42no—
468C3×Dic3—62no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—121no—
478C3×Dic3—121no—
479C3×Dic3—121no—
480C3×Dic3—121no—
481#126—272no—
482#125—91no—
483#124—271no—
484#123—272no—
485C22⋊Q8—91no—
486#121—271no—
487C4×Q8—91no—
488C4×D4—272no—
489C4×D4—271no—
490#117—272no—
491C2×C42—271no—
492C33#52911yescharacteristic, complemented, Sylow
493C23×C3—91no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—61no—
497C22×D3—92no—
498C22×D3—92no—
499C22×D3—92no—
500C22×D3—182no—
501C22×D3—182no—
502C22×D3—182no—
503C22×D3—362no—
504C3×Q8—62no—
505C3×Q8—62no—
506C3×Q8—122no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—41no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—182no—
526C2×C3×C4C2×D3211yescharacteristic
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529#67—184no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—182no—
546C2×Dic3—182no—
547C2×Dic3C2×D3212yes—
548C2×Dic3C2×D3212yes—
549C2×Dic3C2×D3212yes—
550D12—184no—
551D12—184no—
552D12—184no—
553D12—182no—
554D12—182no—
555D12—182no—
556D12—362no—
557D12—362no—
558D12—364no—
559D12—364no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—122no—
563C4×D3—184no—
564C4×D3—184no—
565C4×D3—184no—
566C4×D3—182no—
567C4×D3—182no—
568C4×D3—182no—
569C4×D3—182no—
570C4×D3—364no—
571Dic6—22no—
572C2×C32—21no—
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—41no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32C2×#23511yescharacteristic
585C2×C32C2×#23711yescharacteristic
586C2×C32C2×#23911yescharacteristic
587C2×C32C2×#23911yescharacteristic
588C2×C32C2×#23911yescharacteristic
589C2×C32D3×#4111yescharacteristic
590C2×C32D3×#4111yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C3⋊D3—22no—
594C3⋊D3—122no—
595C3⋊D3—124no—
596C3⋊D3—122no—
597C3⋊D3—122no—
598C3⋊D3—242no—
599C3⋊D3—242no—
600C3⋊D3—244no—
601C3×D3—62no—
602C3×D3—62no—
603C3×D3—122no—
604C2×Q8—31no—
605C2×D4—272no—
606C2×D4—271no—
607C22×C4—91no—
608C22×C4—272no—
609C22×C4—271no—
610C22×C4—271no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—92no—
614C4⋊C4—92no—
615C4⋊C4—92no—
616C4⋊C4—92no—
617C22⋊C4—92no—
618C22⋊C4—272no—
619C22⋊C4—272no—
620C22⋊C4—272no—
621C22⋊C4—272no—
622C42—92no—
623C42—91no—
624C42—91no—
625C42—271no—
626C42—271no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—92no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3C22×D3211yescharacteristic
635C22×C3C22×D3211yescharacteristic
636C22×C3C22×D3211yescharacteristic
637C2×D3—32no—
638C2×D3—32no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—184no—
647C2×D3—182no—
648C2×D3—182no—
649C2×D3—182no—
650C2×D3—182no—
651C2×D3—182no—
652C2×D3—182no—
653C2×D3—182no—
654C2×D3—182no—
655C2×D3—182no—
656C2×D3—362no—
657C2×D3—362no—
658C2×D3—362no—
659C2×D3—362no—
660C2×D3—362no—
661C2×D3—362no—
662C2×D3—362no—
663C2×D3—362no—
664C2×D3—364no—
665C2×D3—722no—
666C2×D3—722no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—42no—
671C3×C4—62no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—62no—
676C3×C4—62no—
677C3×C4—92no—
678C3×C4—122no—
679C3×C4—122no—
680C3×C4—122no—
681C3×C4—181no—
682C3×C4—181no—
683C3×C4—181no—
684C3×C4—181no—
685C3×C4#379612yes—
686C3×C4#379912yes—
687C3×C4#380412yes—
688Dic3—22no—
689Dic3—22no—
690Dic3—22no—
691Dic3—32no—
692Dic3—32no—
693Dic3—62no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706C32—21no—
707C32—21no—
708C32—21no—
709C32—41no—
710C32#558011yescharacteristic, complemented
711C32#562411yescharacteristic, complemented
712C32#569111yescharacteristic, complemented
713C23—91no—
714C23—272no—
715Q8—62no—
716D4—544no—
717D4—542no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—182no—
727C2×C4—544no—
728C2×C4—542no—
729C2×C4—542no—
730C2×C4D3311yescharacteristic
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—41no—
743C2×C3—182no—
744C2×C3C2×#379611yescharacteristic
745C2×C3C2×#379911yescharacteristic
746C2×C3#6431211yescharacteristic
747C2×C3#6431211yescharacteristic
748C2×C3D3×#23911yescharacteristic
749C2×C3D3×#23911yescharacteristic
750C2×C3D3×#23911yescharacteristic
751C2×C3D3×#23911yescharacteristic
752C2×C3C2×#380411yescharacteristic
753D3—62no—
754D3—62no—
755D3—122no—
756D3—364no—
757D3—362no—
758D3—362no—
759D3—362no—
760D3—722no—
761D3—722no—
762D3—724no—
763C22—92no—
764C22—181no—
765C22—181no—
766C22—542no—
767C22—542no—
768C22—542no—
769C22C2×D3311yescharacteristic
770C4—62no—
771C4—62no—
772C4—62no—
773C4—92no—
774C4—181no—
775C4—181no—
776C4—181no—
777C4—181no—
778C4#8896212yes—
779C3—21no—
780C3—21no—
781C3—21no—
782C3—41no—
783C3#1059445311yescharacteristic, complemented
784C3#1059446411yescharacteristic, complemented
785C3#1059537611yescharacteristic, complemented
786C2—182no—
787C2—1082no—
788C2#1172437711yescharacteristic
789C2#1172437711yescharacteristic
790C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11723526C2
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
1. C4×#6294C2semidirect
3. #11723494C2semidirect
4. #11723440C2semidirect
5. C3×#63872C2semidirect
6. C3×#63871C2semidirect
7. C3×#63843C2semidirect
8. #11723028C2semidirect
9. #11722999C2semidirect
10. #11722937C2semidirect
11. #11722920C2semidirect
62. #63872D3semidirect
63. #63871D3semidirect
71. #63843D3semidirect
492. C33#529semidirect
710. C32#5580semidirect
711. C32#5624semidirect
712. C32#5691semidirect
783. C3#10594453semidirect
784. C3#10594464semidirect
785. C3#10595376semidirect

Maximal subgroups

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

subgroupindex
C4×#62942
#117235262
#117234942
#117234402
C3×#638722
C3×#638712
C3×#638432
#117230282
#117229992
#117229372
#117229202
#105953763
#105944643
#105944533