Finite Group Databasebeta

← #10801350

Subgroups — #10801350

Order 768.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4706C211yesmaximal, characteristic, complemented
2C2×#4706C211yesmaximal, characteristic, complemented
3C2×#4708C211yesmaximal, characteristic, complemented
4C2×#4688C211yesmaximal, characteristic, complemented
5#73776C211yesmaximal, characteristic
6C3×#1771C211yesmaximal, characteristic, complemented
7#70476C211yesmaximal, characteristic, complemented
8#70470C211yesmaximal, characteristic, complemented
9#69808C211yesmaximal, characteristic, complemented
10C8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#69484C211yesmaximal, characteristic, complemented
12#68668C211yesmaximal, characteristic, complemented
13#68668C211yesmaximal, characteristic, complemented
14#68616C211yesmaximal, characteristic, complemented
15#68616C211yesmaximal, characteristic, complemented
16#21496—31nomaximal, Sylow
17C22×ΓL(1,𝔽25)C2211yescharacteristic
18C22×ΓL(1,𝔽25)C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×C4×D12C2211yescharacteristic
22C2×C4×D12C2211yescharacteristic
23C2×C4×D12C2211yescharacteristic
24C2×#872C2211yescharacteristic
25C2×C3×C4⋊C8C2211yescharacteristic
26C2×C3×#97C2211yescharacteristic
27C2×C3×#97C2211yescharacteristic
28C2×C3×C4×C8C2211yescharacteristic
29C3×C4×C4⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C8C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×(C2×D3)⋊C8C2211yescharacteristic
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×(C2×D3)⋊C8C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#815C2211yescharacteristic
39C2×C8×Dic3C2211yescharacteristic
40#4994C411yescharacteristic
41#4994C411yescharacteristic
42#4991C411yescharacteristic
43#4991C411yescharacteristic
44C4×(C2×D3)⋊C4C2211yescharacteristic
45C4×(C2×D3)⋊C4C2211yescharacteristic
46C2×C4⋊(C3⋊C8)C2211yescharacteristic
47C2×C4⋊(C3⋊C8)C2211yescharacteristic
48C2×C4⋊(C3⋊C8)C2211yescharacteristic
49C2×C4×C3⋊C8C2211yescharacteristic
50#4708—24no—
51#4706—24no—
52#4706—24no—
53#4688—24no—
54#4674C411yescharacteristic
55#4672C411yescharacteristic
56#4671C411yescharacteristic
57#4661C411yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#436—31no—
65C2×#435—31no—
66C2×#435—31no—
67C2×#405—31no—
68#2392—31no—
69#1954—31no—
70#1939—31no—
71#1924—31no—
72#1924—31no—
73#1869—31no—
74#1869—31no—
75#1798—31no—
76#1771D311yescharacteristic, complemented
77#1753—31no—
78C8×C22⋊C4—31no—
79C22×D12C2×C411yescharacteristic
80C22×D12C2×C411yescharacteristic
81C22×D12C2×C411yescharacteristic
82C22×C4×D3C2311yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C2×C3×C4⋊C4C2×C411yescharacteristic
90C2×C3×C4⋊C4C2×C411yescharacteristic
91C2×C3×C42C2311yescharacteristic
92C2×C3×C42C2311yescharacteristic
93C2×C3×C42C2311yescharacteristic
94C2×(C2×D3)⋊C4C2×C411yescharacteristic
95C2×(C2×D3)⋊C4C2×C411yescharacteristic
96C2×(C2×D3)⋊C4C2×C411yescharacteristic
97C2×(C2×D3)⋊C4C2×C411yescharacteristic
98C2×(C2×D3)⋊C4C2×C411yescharacteristic
99C2×(C2×D3)⋊C4C2×C411yescharacteristic
100C2×(C2×D3)⋊C4C2×C411yescharacteristic
101C2×(C2×D3)⋊C4C2×C411yescharacteristic
102C2×(C2×D3)⋊C4C2×C411yescharacteristic
103C2×(C2×D3)⋊C4C2×C411yescharacteristic
104C2×(C2×D3)⋊C4C2×C411yescharacteristic
105C2×(C2×D3)⋊C4C2×C411yescharacteristic
106C2×C4⋊Dic3C2×C411yescharacteristic
107C2×C4⋊Dic3C2×C411yescharacteristic
108C2×C4⋊Dic3C2×C411yescharacteristic
109C2×Dic3⋊C4C2×C411yescharacteristic
110C2×Dic3⋊C4C2×C411yescharacteristic
111C2×C4×Dic3C2311yescharacteristic
112C22×C3⋊C8C2311yescharacteristic
113C22×C3⋊C8C2311yescharacteristic
114C22×C3⋊C8C2311yescharacteristic
115C22×C3⋊C8C2311yescharacteristic
116C2×ΓL(1,𝔽25)—22no—
117C2×ΓL(1,𝔽25)—22no—
118C2×ΓL(1,𝔽25)—22no—
119C2×ΓL(1,𝔽25)—22no—
120C2×ΓL(1,𝔽25)—22no—
121C2×ΓL(1,𝔽25)D414yescomplemented
122C2×D3×C8—22no—
123C2×D3×C8—22no—
124C2×D3×C8—22no—
125C2×D3×C8—22no—
126C2×D3×C8—22no—
127C2×D3×C8—22no—
128C4×D12—22no—
129C4×D12—22no—
130C4×D12—22no—
131C4×D12—22no—
132C4×D12—22no—
133C4×D12—22no—
134#872—22no—
135#872—22no—
136C3×C4⋊C8—22no—
137C3×#97—22no—
138C3×#97D414yescomplemented
139C3×C4×C8—22no—
140C3×#95C2×C411yescharacteristic
141C3×#95C2×C411yescharacteristic
142C3⋊#95C2×C411yescharacteristic
143C3⋊#95C2×C411yescharacteristic
144C3⋊#95C2×C411yescharacteristic
145C3⋊#95C2×C411yescharacteristic
146(C2×D3)⋊C8—22no—
147(C2×D3)⋊C8—22no—
148(C2×D3)⋊C8—22no—
149(C2×D3)⋊C8—22no—
150(C2×D3)⋊C8—22no—
151(C2×D3)⋊C8—22no—
152(C2×D3)⋊C8—22no—
153(C2×D3)⋊C8—22no—
154#815—22no—
155C8×Dic3—22no—
156C4⋊(C3⋊C8)—22no—
157C4⋊(C3⋊C8)—22no—
158C4⋊(C3⋊C8)—22no—
159C4×C3⋊C8—22no—
160C22×M16—31no—
161C22×M16—31no—
162C23×C8—31no—
163C23×C8—31no—
164C2×C4×D4—31no—
165C2×C4×D4—31no—
166C2×C4×D4—31no—
167C2×#117—31no—
168#436—64no—
169#435—64no—
170#435—64no—
171C2×C4⋊C8—31no—
172C2×C4⋊C8—31no—
173C2×C4⋊C8—31no—
174C2×C4⋊C8C2×D311yescharacteristic
175C2×C22⋊C8—31no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—31no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8—31no—
181C2×C22⋊C8—31no—
182C2×C22⋊C8—31no—
183#405—64no—
184C2×#97—31no—
185C2×#97C2×D311yescharacteristic
186C2×#97C2×D311yescharacteristic
187C2×C4×C8—31no—
188C2×C4×C8—31no—
189C2×C4×C8C2×D311yescharacteristic
190#398—31no—
191#397—31no—
192#396—31no—
193#396—31no—
194#394—31no—
195#394—31no—
196#394—31no—
197#392—31no—
198C4×C4⋊C4C2×D311yescharacteristic
199C4×C22⋊C4—31no—
200C4×C22⋊C4—31no—
201#336—31no—
202#336—31no—
203#336—31no—
204#336—31no—
205#336C2×D311yescharacteristic
206#336C2×D311yescharacteristic
207C23×D3C22×C411yescharacteristic
208C23×D3C22×C411yescharacteristic
209C23×D3C22×C411yescharacteristic
210C22×C3×C4C22×C411yescharacteristic
211C22×C3×C4C22×C411yescharacteristic
212C22×C3×C4C22×C411yescharacteristic
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C22×C411yescharacteristic
216C22×C3×C4C2411yescharacteristic
217C22×Dic3C22×C411yescharacteristic
218C22×Dic3C22×C411yescharacteristic
219C22×Dic3C22×C411yescharacteristic
220C22×Dic3C22×C411yescharacteristic
221C22×Dic3C22×C411yescharacteristic
222C2×D12—22no—
223C2×D12—22no—
224C2×D12—22no—
225C2×D12—22no—
226C2×D12—22no—
227C2×D12—22no—
228C2×D12—41no—
229C2×D12—41no—
230C2×D12—41no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—21no—
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3C2×D412yes—
248C2×C4×D3#4112yes—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8C2×D412yes—
258C2×C3×C8C2×D412yes—
259C2×C3×C8C2×D412yes—
260C2×C3×C8#4112yes—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—41no—
263C3×C42—21no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42C2×D412yes—
268C3×C42#4112yes—
269(C2×D3)⋊C4—22no—
270(C2×D3)⋊C4—22no—
271(C2×D3)⋊C4—22no—
272(C2×D3)⋊C4—22no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—41no—
280(C2×D3)⋊C4—41no—
281C4⋊Dic3—22no—
282C4⋊Dic3—22no—
283C4⋊Dic3—22no—
284Dic3⋊C4—22no—
285Dic3⋊C4—22no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8C2×D412yes—
299C2×C3⋊C8#4112yes—
300ΓL(1,𝔽25)—28no—
301ΓL(1,𝔽25)—44no—
302D3×C8—28no—
303D3×C8—44no—
304C22×D4—31no—
305C22×D4—31no—
306C22×D4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—31no—
310C2×M16—34no—
311C2×M16—62no—
312C2×M16—62no—
313C2×M16—62no—
314C2×M16—62no—
315C2×M16—62no—
316C22×C8—31no—
317C22×C8—31no—
318C22×C8—31no—
319C22×C8—31no—
320C22×C8—62no—
321C22×C8—62no—
322C22×C8—62no—
323C22×C8—62no—
324C22×C8—62no—
325C22×C8—62no—
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329C22×C8C22×D311yescharacteristic
330C4×D4—62no—
331C4×D4—62no—
332C4×D4—62no—
333C4×D4—62no—
334C4×D4—62no—
335C4×D4—62no—
336#117—62no—
337#117—62no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4C4×D311yescharacteristic
344C2×C4⋊C4C4×D311yescharacteristic
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—31no—
353C2×C22⋊C4—31no—
354C2×C22⋊C4—31no—
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C42—31no—
358C2×C42C22×D311yescharacteristic
359C2×C42C22×D311yescharacteristic
360C2×C42C22×D311yescharacteristic
361C4⋊C8—22no—
362C4⋊C8—62no—
363C4⋊C8—62no—
364C4⋊C8—62no—
365C22⋊C8—62no—
366C22⋊C8—62no—
367C22⋊C8—62no—
368C22⋊C8—62no—
369C22⋊C8—62no—
370C22⋊C8—62no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373#97—22no—
374#97—62no—
375#97D1214yescomplemented
376C4×C8—22no—
377C4×C8—62no—
378C4×C8—62no—
379#95—31no—
380#95—31no—
381#95—31no—
382#95—31no—
383#95C4×D311yescharacteristic
384#95C4×D311yescharacteristic
385C23×C3C23×C411yescharacteristic
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3C4×D412yes—
406C22×D3#13112yes—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4C4×D412yes—
423C2×C3×C4C4×D412yes—
424C2×C3×C4#13112yes—
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3C4×D412yes—
446D12—44no—
447D12—44no—
448D12—44no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—22no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—41no—
456C4×D3—41no—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C3×C8—22no—
462C3×C8—41no—
463C3×C8—41no—
464C3×C8#12114yes—
465C3⋊C8—22no—
466C3⋊C8—22no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C24—31no—
470C24—31no—
471C24—31no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—121no—
479C2×D4—121no—
480C2×D4—121no—
481C22×C4—31no—
482C22×C4—32no—
483C22×C4—32no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4C2×C4×D311yescharacteristic
505C22×C4C2×C4×D311yescharacteristic
506C22×C4C2×C4×D311yescharacteristic
507C22×C4C2×C4×D311yescharacteristic
508C22×C4C2×C4×D311yescharacteristic
509C22×C4C2×C4×D311yescharacteristic
510C22×C4C23×D311yescharacteristic
511M16—68no—
512M16—124no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—32no—
522C2×C8—32no—
523C2×C8—68no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—124no—
535C2×C8C2×D1212yes—
536C2×C8C2×D1212yes—
537C2×C8D3×D412yes—
538C2×C8#23912yes—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—62no—
542C4⋊C4—62no—
543C4⋊C4—62no—
544C4⋊C4—62no—
545C4⋊C4—62no—
546C22⋊C4—62no—
547C22⋊C4—62no—
548C22⋊C4—62no—
549C22⋊C4—62no—
550C22⋊C4—62no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—62no—
556C22⋊C4—121no—
557C22⋊C4—121no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—61no—
563C42—61no—
564C42C2×D1212yes—
565C42#23512yes—
566C22×C3C2×C4×D411yescharacteristic
567C22×C3C2×C4×D411yescharacteristic
568C22×C3C4×#4111yescharacteristic
569C22×C3C2×#13111yescharacteristic
570C22×C3C2×#13111yescharacteristic
571C22×C3#56811yescharacteristic
572C22×C3#56811yescharacteristic
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3—41no—
580C2×D3—41no—
581C2×D3—41no—
582C2×D3—41no—
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4C2×#12111yescharacteristic
601C3×C4#52511yescharacteristic
602C3×C4#52911yescharacteristic
603C3×C4#53211yescharacteristic
604Dic3—22no—
605Dic3—41no—
606Dic3—41no—
607Dic3—41no—
608Dic3—41no—
609C23—32no—
610C23—32no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23C22×C4×D311yescharacteristic
631D4—124no—
632D4—124no—
633D4—124no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—32no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4C4×D1212yes—
677C2×C4C4×D1212yes—
678C2×C4#90712yes—
679C2×C4C22×D1211yescharacteristic
680C2×C4C2×#23511yescharacteristic
681C2×C4C2×D3×D411yescharacteristic
682C2×C4C2×#23911yescharacteristic
683C2×C4D3×#4111yescharacteristic
684C2×C4D3×#4111yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—62no—
689C8—62no—
690C8—121no—
691C8—121no—
692C8#89514yes—
693C2×C3C4×#12111yescharacteristic
694C2×C3#293311yescharacteristic
695C2×C3#293311yescharacteristic
696C2×C3#293311yescharacteristic
697C2×C3#293511yescharacteristic
698C2×C3#296611yescharacteristic
699C2×C3#296711yescharacteristic
700D3—42no—
701D3—42no—
702D3—81no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—62no—
707C22—62no—
708C22—62no—
709C22—121no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22C2×C4×D1211yescharacteristic
725C22C4×D3×D411yescharacteristic
726C22C4×#23911yescharacteristic
727C22C2×#90711yescharacteristic
728C22#574511yescharacteristic
729C22D3×#13111yescharacteristic
730C22#575011yescharacteristic
731C4—22no—
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4C2×#89511yescharacteristic
743C4#552411yescharacteristic
744C4#554811yescharacteristic
745C4#558011yescharacteristic
746C3#2149611yescharacteristic, complemented, Sylow
747C2—122no—
748C2—122no—
749C2—241no—
750C2C4×#89511yescharacteristic
751C2#7852211yescharacteristic
752C2#7855511yescharacteristic
753C2#7948111yescharacteristic
754C2#7948211yescharacteristic
755C2#7993911yescharacteristic
756C2#7994011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1771C2
prime radical#4671C4
cosocleC22×C3×C4C24
hypercenter#1771D3
hypocenterC3#21496
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. C2×#4706C2semidirect
2. C2×#4706C2semidirect
3. C2×#4708C2semidirect
4. C2×#4688C2semidirect
6. C3×#1771C2semidirect
7. #70476C2semidirect
8. #70470C2semidirect
9. #69808C2semidirect
10. C8×(C2×D3)⋊C4C2semidirect
11. #69484C2semidirect
12. #68668C2semidirect
13. #68668C2semidirect
14. #68616C2semidirect
15. #68616C2semidirect
76. #1771D3semidirect
121. C2×ΓL(1,𝔽25)D4semidirect
138. C3×#97D4semidirect
375. #97D12semidirect
746. C3#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#47062
C2×#47082
C2×#46882
#737762
C3×#17712
#704762
#704702
#698082
C8×(C2×D3)⋊C42
#694842
#686682
#686162
#214963