Finite Group Databasebeta

← #10804117

Subgroups — #10804117

Order 768.

1426 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5548C211yesmaximal, characteristic
2C2×#5129C211yesmaximal, characteristic, complemented
3C2×#4727C211yesmaximal, characteristic, complemented
4C3×#1870C211yesmaximal, characteristic, complemented
5#71996C211yesmaximal, characteristic, complemented
6#71610C211yesmaximal, characteristic, complemented
7#69958C211yesmaximal, characteristic, complemented
8#69957C211yesmaximal, characteristic, complemented
9#69956C211yesmaximal, characteristic, complemented
10#69956C211yesmaximal, characteristic, complemented
11#69952C211yesmaximal, characteristic, complemented
12#68669C211yesmaximal, characteristic, complemented
13#68668C211yesmaximal, characteristic, complemented
14#68664C211yesmaximal, characteristic, complemented
15#68664C211yesmaximal, characteristic, complemented
16#21745—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#940C411yescharacteristic
22C2×#938C411yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5548—24no—
29#5548—24no—
30C2×#895C411yescharacteristic
31C2×#888C411yescharacteristic
32C2×#885C411yescharacteristic
33C2×#885C411yescharacteristic
34C2×#884C411yescharacteristic
35C2×#884C411yescharacteristic
36C2×C4×D12C2211yescharacteristic
37C2×C42×D3C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5129—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55#4727—24no—
56C3×#336C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#532—31no—
65C2×#408—31no—
66C2×#408—31no—
67#1870—31no—
68#1870—31no—
69#1870—31no—
70#1870D311yescharacteristic, complemented
71#1869—31no—
72#1869—31no—
73#1869—31no—
74#1869—31no—
75#1817—31no—
76#1817—31no—
77#1780—31no—
78#1780—31no—
79C22×C3×D4C2×C411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67C2×C411yescharacteristic
83C22×#67C2×C411yescharacteristic
84C22×#67C2×C411yescharacteristic
85C22×#67C2×C411yescharacteristic
86C22×#67C2×C411yescharacteristic
87C22×#67C2×C411yescharacteristic
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—41no—
91C2×#235—41no—
92C2×#235—41no—
93C2×#235—41no—
94C2×#235—41no—
95C2×#235—41no—
96C2×#235—41no—
97C2×#235—41no—
98C2×#235D414yes—
99C2×#235D414yes—
100C22×D12C2×C411yescharacteristic
101C22×D12C2×C411yescharacteristic
102C22×D12C2×C411yescharacteristic
103C22×C4×D3C2×C411yescharacteristic
104C22×C4×D3C2×C411yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×C4×D3C2311yescharacteristic
108C22×Dic6C2×C411yescharacteristic
109C22×Dic6C2×C411yescharacteristic
110C2×C3×M16—22no—
111C2×C3×M16—41no—
112C2×C3×M16—41no—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C2×C3×C4⋊C4C2×C411yescharacteristic
120C2×C3×C22⋊C4C2×C411yescharacteristic
121C2×C3×C22⋊C4C2×C411yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217C2×C411yescharacteristic
124C2×#217C2×C411yescharacteristic
125#940—24no—
126#938—24no—
127C4×#67—22no—
128C4×#67—22no—
129C4×#67—22no—
130C4×#67—22no—
131C2×(C2×D3)⋊C4C2×C411yescharacteristic
132C2×(C2×D3)⋊C4C2×C411yescharacteristic
133C2×(C2×D3)⋊C4C2×C411yescharacteristic
134C2×(C2×D3)⋊C4C2×C411yescharacteristic
135C2×C4⋊Dic3C2×C411yescharacteristic
136C2×Dic3⋊C4C2×C411yescharacteristic
137C2×Dic3⋊C4C2×C411yescharacteristic
138C2×C4×Dic3C2×C411yescharacteristic
139C2×C4×Dic3C2×C411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8—22no—
142C22×C3⋊C8—41no—
143C22×C3⋊C8—41no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—41no—
150C2×ΓL(1,𝔽25)—41no—
151C2×D3×C8—22no—
152C2×D3×C8—41no—
153C2×D3×C8—41no—
154#895—24no—
155#888—24no—
156#885—24no—
157#885—24no—
158#884—24no—
159#884—24no—
160C4×D12—22no—
161C4×D12—22no—
162C42×D3—22no—
163C42×D3—22no—
164C3×C22⋊C8—22no—
165C3×C22⋊C8—41no—
166C3×C22⋊C8—41no—
167#830—22no—
168#830—41no—
169#830—41no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177(C2×D3)⋊C8—41no—
178(C2×D3)⋊C8—41no—
179(C2×D3)⋊C8—41no—
180C22×#41—31no—
181C22×#41—31no—
182C22×M16—31no—
183C22×M16C2×D311yescharacteristic
184C23×C8—31no—
185C23×C8—31no—
186#532—64no—
187#532—64no—
188C2×C4⋊Q8—31no—
189C2×#127—31no—
190C2×#124—31no—
191C2×#124—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—31no—
196C2×C4×D4—31no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C22×C42—31no—
201#408—64no—
202#408—64no—
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8—31no—
206C2×C22⋊C8—31no—
207C2×C22⋊C8—31no—
208C2×C22⋊C8—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214C2×C22⋊C8—31no—
215C2×C22⋊C8—31no—
216C2×C22⋊C8C2×D311yescharacteristic
217C2×C22⋊C8C2×D311yescharacteristic
218C2×C22⋊C8C2×D311yescharacteristic
219#336—31no—
220#336—31no—
221#336—31no—
222#336—31no—
223#336—31no—
224#336—31no—
225#336C2×D311yescharacteristic
226#336C2×D311yescharacteristic
227C24×C3C22×C411yescharacteristic
228C24×C3C22×C411yescharacteristic
229C23×D3C22×C411yescharacteristic
230C23×D3C22×C411yescharacteristic
231C23×D3C22×C411yescharacteristic
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—41no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C411yescharacteristic
247C22×C3×C4C22×C411yescharacteristic
248C22×C3×C4C22×C411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2411yescharacteristic
252C2×#67—22no—
253C2×#67—22no—
254C2×#67—22no—
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—22no—
258C2×#67—41no—
259C2×#67—41no—
260C2×#67—41no—
261C2×#67—41no—
262C2×#67—41no—
263C2×#67—41no—
264C2×#67—41no—
265C2×#67—41no—
266C2×#67—41no—
267C2×#67—41no—
268C2×#67C22⋊C414yes—
269C2×#67C22⋊C414yes—
270C22×Dic3C22×C411yescharacteristic
271C22×Dic3C22×C411yescharacteristic
272C22×Dic3C22×C411yescharacteristic
273C22×Dic3C22×C411yescharacteristic
274C22×Dic3C22×C411yescharacteristic
275#235—44no—
276#235—44no—
277#235—44no—
278#235—44no—
279#235—44no—
280#235—44no—
281#235—44no—
282#235—44no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—22no—
286C2×D12—41no—
287C2×D12—41no—
288C2×D12—41no—
289C2×D12—41no—
290C2×D12—41no—
291C2×D12C22⋊C414yes—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—22no—
310C2×C4×D3—41no—
311C2×C4×D3—41no—
312C2×C4×D3C2×D412yes—
313C2×C4×D3C2×D412yes—
314C2×C4×D3C2×D412yes—
315C2×C4×D3C2×D412yes—
316C2×Dic6—22no—
317C2×Dic6—41no—
318C2×Dic6—41no—
319C2×Dic6—41no—
320C2×Dic6—41no—
321C2×Dic6C22⋊C414yes—
322C3×M16—44no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C3×C4⋊C4—22no—
336C3×C22⋊C4—22no—
337C3×C22⋊C4—22no—
338C3×C42—21no—
339C3×C42—21no—
340#217—22no—
341#217—22no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—22no—
346C4⋊Dic3—22no—
347Dic3⋊C4—22no—
348Dic3⋊C4—22no—
349C4×Dic3—21no—
350C4×Dic3—21no—
351C4×Dic3—22no—
352C4×Dic3—22no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8—21no—
363C2×C3⋊C8—21no—
364C2×C3⋊C8—21no—
365C2×C3⋊C8—44no—
366ΓL(1,𝔽25)—44no—
367D3×C8—44no—
368C2×#41—34no—
369C2×#41—34no—
370C2×#41—62no—
371C2×#41—62no—
372C2×#41—121no—
373C2×#41—121no—
374C2×#41—121no—
375C2×#41—121no—
376C2×#41—121no—
377C2×#41—121no—
378C2×#41—121no—
379C2×#41—121no—
380C22×Q8—31no—
381C22×Q8—31no—
382C22×D4—31no—
383C22×D4—31no—
384C22×D4—31no—
385C22×D4—31no—
386C22×D4—31no—
387C22×D4—31no—
388C22×D4—31no—
389C22×D4—31no—
390C22×D4—31no—
391C22×D4C4×D311yescharacteristic
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C2×M16—22no—
400C2×M16—41no—
401C2×M16—41no—
402C2×M16—62no—
403C2×M16—121no—
404C2×M16—121no—
405C22×C8—31no—
406C22×C8—31no—
407C22×C8—31no—
408C22×C8—31no—
409C22×C8—62no—
410C22×C8—62no—
411C22×C8—121no—
412C22×C8—121no—
413C22×C8—121no—
414C22×C8—121no—
415C22×C8C22×D311yescharacteristic
416C22×C8C22×D311yescharacteristic
417C22×C8C22×D311yescharacteristic
418C22×C8C22×D311yescharacteristic
419C4⋊Q8—64no—
420#127—64no—
421#124—64no—
422#124—64no—
423#121—64no—
424#121—64no—
425#121—64no—
426#121—64no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—62no—
430C4×D4—62no—
431C4×D4—62no—
432C4×D4—62no—
433C4×D4—62no—
434C4×D4—62no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4C4×D311yescharacteristic
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4C4×D311yescharacteristic
446C2×C22⋊C4C4×D311yescharacteristic
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—62no—
451C2×C42—62no—
452C2×C42C22×D311yescharacteristic
453C22⋊C8—22no—
454C22⋊C8—41no—
455C22⋊C8—41no—
456C22⋊C8—62no—
457C22⋊C8—62no—
458C22⋊C8—62no—
459C22⋊C8—62no—
460C22⋊C8—62no—
461C22⋊C8—62no—
462C22⋊C8—62no—
463C22⋊C8—121no—
464C22⋊C8—121no—
465C22⋊C8—121no—
466C22⋊C8—121no—
467C22⋊C8—121no—
468C22⋊C8—121no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3C2×C22⋊C412yes—
483C23×C3C23×C411yescharacteristic
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3C2×C22⋊C412yes—
504C22×D3C2×C22⋊C412yes—
505C3×D4—44no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4C2×C22⋊C412yes—
525C2×C3×C4#13112yes—
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4H(5,𝔽2)11yescharacteristic
529C2×C3×C4H(5,𝔽2)11yescharacteristic
530C2×C3×C4H(5,𝔽2)11yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532#67—44no—
533#67—44no—
534#67—44no—
535#67—44no—
536#67—44no—
537#67—44no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3C2×C22⋊C412yes—
551C2×Dic3C2×C22⋊C412yes—
552C2×Dic3#13112yes—
553D12—44no—
554D12—44no—
555D12—44no—
556C4×D3—22no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—22no—
560C4×D3—22no—
561C4×D3—22no—
562C4×D3—22no—
563C4×D3—22no—
564C4×D3—44no—
565C4×D3—44no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—41no—
569C4×D3—41no—
570Dic6—44no—
571Dic6—44no—
572C3×C8—41no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—41no—
576C3⋊C8—41no—
577C3⋊C8—41no—
578C3⋊C8—41no—
579C3⋊C8—41no—
580C24—31no—
581C24—31no—
582C24—31no—
583C24C2×C4×D311yescharacteristic
584C24C2×C4×D311yescharacteristic
585#41—124no—
586#41—124no—
587#41—124no—
588#41—124no—
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—34no—
594C2×Q8—62no—
595C2×Q8—121no—
596C2×Q8—121no—
597C2×Q8—121no—
598C2×Q8—121no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—34no—
602C2×D4—34no—
603C2×D4—34no—
604C2×D4—41no—
605C2×D4—62no—
606C2×D4—62no—
607C2×D4—62no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—62no—
611C2×D4—62no—
612C2×D4—62no—
613C2×D4—62no—
614C2×D4—121no—
615C2×D4—121no—
616C2×D4—121no—
617C2×D4—121no—
618C2×D4—121no—
619C2×D4—121no—
620C2×D4—121no—
621C2×D4—121no—
622C2×D4—121no—
623C2×D4—121no—
624C2×D4—121no—
625C2×D4—121no—
626C2×D4—121no—
627C2×D4—121no—
628C2×D4—121no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—62no—
649C22×C4—62no—
650C22×C4—62no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—62no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—121no—
667C22×C4—121no—
668C22×C4C2×C4×D311yescharacteristic
669C22×C4C2×C4×D311yescharacteristic
670C22×C4C2×C4×D311yescharacteristic
671C22×C4C2×C4×D311yescharacteristic
672C22×C4D3×D412yes—
673C22×C4D3×D412yes—
674C22×C4C23×D311yescharacteristic
675M16—44no—
676M16—124no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—61no—
690C2×C8—61no—
691C2×C8—61no—
692C2×C8—61no—
693C2×C8—61no—
694C2×C8—61no—
695C2×C8—61no—
696C2×C8—61no—
697C2×C8—61no—
698C2×C8—61no—
699C2×C8—61no—
700C2×C8—61no—
701C2×C8—124no—
702C2×C8—124no—
703C4⋊C4—22no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—62no—
710C22⋊C4—62no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C42—21no—
716C42—21no—
717C42—62no—
718C42—62no—
719C42—61no—
720C42—61no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3C22×C22⋊C411yescharacteristic
736C22×C3#51811yescharacteristic
737C22×C3#51811yescharacteristic
738C22×C3C2×#13111yescharacteristic
739C22×C3C2×#13111yescharacteristic
740C22×C3#56811yescharacteristic
741C22×C3#56811yescharacteristic
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4#53411yescharacteristic
768C3×C4#53411yescharacteristic
769C3×C4#53411yescharacteristic
770C3×C4#53411yescharacteristic
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—41no—
775Dic3—41no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—32no—
790C23—32no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—61no—
795C23—61no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23D3×C22⋊C412yes—
811C23C22×C4×D311yescharacteristic
812Q8—124no—
813Q8—124no—
814D4—44no—
815D4—124no—
816D4—124no—
817D4—124no—
818D4—124no—
819D4—124no—
820D4—124no—
821D4—124no—
822D4—124no—
823D4—124no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4D3×C22⋊C412yes—
872C2×C4#90712yes—
873C2×C4C2×D3×D411yescharacteristic
874C2×C4C2×D3×D411yescharacteristic
875C2×C4#100411yescharacteristic
876C2×C4#100411yescharacteristic
877C2×C4#100911yescharacteristic
878C2×C4#100911yescharacteristic
879C8—41no—
880C8—41no—
881C8—41no—
882C8—41no—
883C8—121no—
884C8—121no—
885C8—121no—
886C8—121no—
887C2×C3—42no—
888C2×C3—81no—
889C2×C3#230811yescharacteristic
890C2×C3#288011yescharacteristic
891C2×C3#288011yescharacteristic
892C2×C3#297911yescharacteristic
893C2×C3#298011yescharacteristic
894C2×C3#298111yescharacteristic
895C2×C3#298111yescharacteristic
896D3—42no—
897D3—42no—
898D3—81no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22C2×D3×C22⋊C411yescharacteristic
935C22#554511yescharacteristic
936C22#554511yescharacteristic
937C22C2×#90711yescharacteristic
938C22#574511yescharacteristic
939C22D3×#13111yescharacteristic
940C22#575011yescharacteristic
941C4—22no—
942C4—22no—
943C4—41no—
944C4—41no—
945C4—62no—
946C4—62no—
947C4—62no—
948C4—121no—
949C4—121no—
950C4#558911yescharacteristic
951C4#560511yescharacteristic
952C4#560511yescharacteristic
953C4#565311yescharacteristic
954C3#2174511yescharacteristic, complemented, Sylow
955C2—42no—
956C2—81no—
957C2—122no—
958C2—122no—
959C2—241no—
960C2#7487411yescharacteristic
961C2#7863111yescharacteristic
962C2#7866311yescharacteristic
963C2#7949111yescharacteristic
964C2#7949211yescharacteristic
965C2#7954611yescharacteristic
966C2#7954711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1870C2
prime radicalC2×#5548C2
cosocleC22×C3×C4C24
hypercenter#1870D3
hypocenterC3#21745
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#5129C2semidirect
3. C2×#4727C2semidirect
4. C3×#1870C2semidirect
5. #71996C2semidirect
6. #71610C2semidirect
7. #69958C2semidirect
8. #69957C2semidirect
9. #69956C2semidirect
10. #69956C2semidirect
11. #69952C2semidirect
12. #68669C2semidirect
13. #68668C2semidirect
14. #68664C2semidirect
15. #68664C2semidirect
70. #1870D3semidirect
954. C3#21745semidirect

Maximal subgroups

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

subgroupindex
C2×#55482
C2×#51292
C2×#47272
C3×#18702
#719962
#716102
#699582
#699572
#699562
#699522
#686692
#686682
#686642
#217453