Finite Group Databasebeta

← #33097982

Subgroups — #33097982

Order 18688.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988718C211yesmaximal, characteristic, complemented
2C2×#17988648C211yesmaximal, characteristic
3#22610868C211yesmaximal, characteristic, complemented
4#22610655C211yesmaximal, characteristic, complemented
5#22610650C211yesmaximal, characteristic, complemented
6#22610650C211yesmaximal, characteristic, complemented
7#22610546C211yesmaximal, characteristic
8#22610546C211yesmaximal, characteristic
9#22610539C211yesmaximal, characteristic
10#22610539C211yesmaximal, characteristic
11#22610497C211yesmaximal, characteristic, complemented
12#22610490C211yesmaximal, characteristic, complemented
13#22609915C211yesmaximal, characteristic
14#22609806C211yesmaximal, characteristic, complemented
15C73×#2396C211yesmaximal, characteristic
16#17988718—24no—
17#17988648—24no—
18C2×C4⋊#10596831C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×C4⋊#10596831C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×#14556502C2211yescharacteristic
31C2×#14556502C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×C4×#10596831C2211yescharacteristic
34C2×C4×#10596831C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36#17988342C2211yescharacteristic
37#17988342C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46C2×C4×Q8×C73C2211yescharacteristic
47C2×#117×C73C2211yescharacteristic
48#400×C73C411yescharacteristic
49#399×C73C411yescharacteristic
50#398×C73C411yescharacteristic
51#398×C73C411yescharacteristic
52#396×C73C411yescharacteristic
53#396×C73C411yescharacteristic
54#395×C73C411yescharacteristic
55#393×C73C411yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59C4×C22⋊C4×C73C2211yescharacteristic
60C4×C22⋊C4×C73C2211yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C4⋊#10596831—22no—
70C4⋊#10596831—22no—
71C4⋊#10596831—22no—
72C4⋊#10596831—22no—
73C4⋊#10596831—22no—
74C4⋊#10596831—22no—
75C4⋊#10596831—41no—
76C4⋊#10596831—41no—
77C22⋊#10596831—22no—
78C22⋊#10596831—22no—
79C22⋊#10596831—41no—
80C22⋊#10596831—41no—
81#14556502—22no—
82#14556502—41no—
83#14556502D414yes—
84C4×#10596831—22no—
85C4×#10596831—22no—
86C4×#10596831—41no—
87C22×Q8×C73C2×C411yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C4×Q8×C73—22no—
90C4×Q8×C73—22no—
91#117×C73—22no—
92#117×C73—22no—
93C2×C4⋊C4×C73C2×C411yescharacteristic
94C2×C4⋊C4×C73C2×C411yescharacteristic
95C2×C4⋊C4×C73C2×C411yescharacteristic
96C2×C4⋊C4×C73C2×C411yescharacteristic
97C2×C4⋊C4×C73C2×C411yescharacteristic
98C2×C4⋊C4×C73C2×C411yescharacteristic
99C2×C4⋊C4×C73C2×C411yescharacteristic
100C2×C4⋊C4×C73C2×C411yescharacteristic
101C2×C4⋊C4×C73C2×C411yescharacteristic
102C2×C4⋊C4×C73C2×C411yescharacteristic
103C2×C4⋊C4×C73C2×C411yescharacteristic
104C2×C22⋊C4×C73C2×C411yescharacteristic
105C2×C22⋊C4×C73C2×C411yescharacteristic
106C2×C22⋊C4×C73C2×C411yescharacteristic
107C2×C22⋊C4×C73C2×C411yescharacteristic
108C2×C22⋊C4×C73C2×C411yescharacteristic
109C2×C22⋊C4×C73C2×C411yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116#95×C73C2×C411yescharacteristic
117#95×C73C2×C411yescharacteristic
118#95×C73C2×C411yescharacteristic
119#95×C73C2×C411yescharacteristic
120#95×C73C2×C411yescharacteristic
121#95×C73C2×C411yescharacteristic
122#95×C73C2×C411yescharacteristic
123#95×C73C2×C411yescharacteristic
124#95×C73C2×C411yescharacteristic
125#95×C73C2×C411yescharacteristic
126C2×#10596831—21no—
127C2×#10596831—21no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831C2×D412yes—
149C2×#10596831C2×D412yes—
150C24×C73C22×C411yescharacteristic
151C2×Q8×C73—22no—
152C2×Q8×C73—22no—
153C2×Q8×C73—41no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73C22×C411yescharacteristic
161C22×C4×C73C22×C411yescharacteristic
162C22×C4×C73C22×C411yescharacteristic
163C22×C4×C73C22×C411yescharacteristic
164C22×C4×C73C22×C411yescharacteristic
165C22×C4×C73C22×C411yescharacteristic
166C22×C4×C73C22×C411yescharacteristic
167C22×C4×C73C22×C411yescharacteristic
168C22×C4×C73C22×C411yescharacteristic
169C22×C4×C73C22×C411yescharacteristic
170C22×C4×C73C22×C411yescharacteristic
171C22×C4×C73C22×C411yescharacteristic
172C22×C4×C73C22×C411yescharacteristic
173C22×C4×C73C2411yescharacteristic
174C4⋊C4×C73—22no—
175C4⋊C4×C73—22no—
176C4⋊C4×C73—22no—
177C4⋊C4×C73—22no—
178C4⋊C4×C73—22no—
179C4⋊C4×C73—22no—
180C4⋊C4×C73—22no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73—41no—
183C4⋊C4×C73—41no—
184C4⋊C4×C73—41no—
185C22⋊C4×C73—22no—
186C22⋊C4×C73—22no—
187C22⋊C4×C73—22no—
188C22⋊C4×C73—22no—
189C22⋊C4×C73—41no—
190C22⋊C4×C73—41no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—21no—
195C42×C73—21no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73C2×D412yes—
202C42×C73#4112yes—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73C23×C411yescharacteristic
211Q8×C73—44no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73C4×D412yes—
252C2×C4×C73C4×D412yes—
253C2×C4×C73#13112yes—
254C2×C4×C73#13112yes—
255C2×C4×C73C22×D411yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C2×C4×C73H(5,𝔽2)11yescharacteristic
258C2×C4×C732−1+411yescharacteristic
259C2×C4×C732−1+411yescharacteristic
260C2×C4×C732−1+411yescharacteristic
261#10596831—22no—
262#10596831—22no—
263#10596831—41no—
264#10596831—41no—
265#10596831—41no—
266#10596831—41no—
267#10596831—41no—
268#10596831—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73C2×C4×D411yescharacteristic
277C22×C73#51911yescharacteristic
278C22×C73#52011yescharacteristic
279C22×C73C2×#13111yescharacteristic
280C22×C73C2×#13111yescharacteristic
281C22×C73#56811yescharacteristic
282C22×C73#56811yescharacteristic
283C4×C73—22no—
284C4×C73—22no—
285C4×C73—22no—
286C4×C73—22no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73—41no—
295C4×C73—41no—
296C4×C73#53611yescharacteristic
297C4×C73#53711yescharacteristic
298C4×C73#54111yescharacteristic
299C4×C73#54211yescharacteristic
300#22107—731nomaximal, Sylow
301C2×C73—81no—
302C2×C73#232311yescharacteristic
303C2×C73#293311yescharacteristic
304C2×C73#293511yescharacteristic
305C2×C73#298511yescharacteristic
306C2×C73#298511yescharacteristic
307C2×C73#299411yescharacteristic
308C2×C73#299511yescharacteristic
309C2×#446—731no—
310C2×#433—731no—
311#2396D7311yescharacteristic
312#1984—731no—
313#1940—731no—
314#1939—731no—
315#1939—731no—
316#1924—731no—
317#1924—731no—
318#1923—731no—
319#1923—731no—
320#1917—731no—
321#1916—731no—
322#1798—731no—
323#1771—731no—
324C73#2210711yescharacteristic, complemented, Sylow
325C2×C4×Q8C2×D7311yescharacteristic
326C2×#117C2×D7311yescharacteristic
327#446—1464no—
328#433—1464no—
329C2×C4⋊C8—731no—
330C2×C4⋊C8—731no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C4⋊C8—731no—
336C2×C4⋊C8—731no—
337C2×C22⋊C8—731no—
338C2×C22⋊C8—731no—
339C2×C22⋊C8—731no—
340C2×C22⋊C8—731no—
341C2×#97—731no—
342C2×#97—731no—
343C2×#97—731no—
344C2×C4×C8—731no—
345C2×C4×C8—731no—
346C2×C4×C8—731no—
347#400Dic7311yescharacteristic
348#399Dic7311yescharacteristic
349#398Dic7311yescharacteristic
350#398Dic7311yescharacteristic
351#396Dic7311yescharacteristic
352#396Dic7311yescharacteristic
353#395Dic7311yescharacteristic
354#393Dic7311yescharacteristic
355C4×C4⋊C4C2×D7311yescharacteristic
356C4×C4⋊C4C2×D7311yescharacteristic
357C4×C4⋊C4C2×D7311yescharacteristic
358C4×C22⋊C4C2×D7311yescharacteristic
359C4×C22⋊C4C2×D7311yescharacteristic
360#336—731no—
361#336—731no—
362#336—731no—
363#336—731no—
364#336—731no—
365#336—731no—
366#336—731no—
367#336—731no—
368#336—731no—
369#336—731no—
370C22×Q8C2×Dic7311yescharacteristic
371C23×C4C22×D7311yescharacteristic
372C22×C8—731no—
373C22×C8—731no—
374C22×C8—731no—
375C22×C8—731no—
376C22×C8—731no—
377C22×C8—731no—
378C22×C8—731no—
379C22×C8—731no—
380C4×Q8—22no—
381C4×Q8—22no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4C2×Dic7311yescharacteristic
385C2×C4⋊C4C2×Dic7311yescharacteristic
386C2×C4⋊C4C2×Dic7311yescharacteristic
387C2×C4⋊C4C2×Dic7311yescharacteristic
388C2×C4⋊C4C2×Dic7311yescharacteristic
389C2×C4⋊C4C2×Dic7311yescharacteristic
390C2×C4⋊C4C2×Dic7311yescharacteristic
391C2×C4⋊C4C2×Dic7311yescharacteristic
392C2×C4⋊C4C2×Dic7311yescharacteristic
393C2×C4⋊C4C2×Dic7311yescharacteristic
394C2×C4⋊C4C2×Dic7311yescharacteristic
395C2×C22⋊C4C2×Dic7311yescharacteristic
396C2×C22⋊C4C2×Dic7311yescharacteristic
397C2×C22⋊C4C2×Dic7311yescharacteristic
398C2×C22⋊C4C2×Dic7311yescharacteristic
399C2×C22⋊C4C2×Dic7311yescharacteristic
400C2×C22⋊C4C2×Dic7311yescharacteristic
401C2×C42C22×D7311yescharacteristic
402C2×C42C22×D7311yescharacteristic
403C2×C42C22×D7311yescharacteristic
404C2×C42C22×D7311yescharacteristic
405C2×C42C22×D7311yescharacteristic
406C2×C42C22×D7311yescharacteristic
407C4⋊C8—2921no—
408C4⋊C8—2921no—
409C4⋊C8—1462no—
410C4⋊C8—1462no—
411C4⋊C8—1462no—
412C4⋊C8—1462no—
413C4⋊C8—1462no—
414C4⋊C8—1462no—
415C22⋊C8—2921no—
416C22⋊C8—2921no—
417C22⋊C8—1462no—
418C22⋊C8—1462no—
419#97—2921no—
420#97—734no—
421#97—1462no—
422C4×C8—2921no—
423C4×C8—1462no—
424C4×C8—1462no—
425#95C2×Dic7311yescharacteristic
426#95C2×Dic7311yescharacteristic
427#95C2×Dic7311yescharacteristic
428#95C2×Dic7311yescharacteristic
429#95C2×Dic7311yescharacteristic
430#95C2×Dic7311yescharacteristic
431#95C2×Dic7311yescharacteristic
432#95C2×Dic7311yescharacteristic
433#95C2×Dic7311yescharacteristic
434#95C2×Dic7311yescharacteristic
435C24C22×Dic7311yescharacteristic
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—41no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C22×Dic7311yescharacteristic
446C22×C4C22×Dic7311yescharacteristic
447C22×C4C22×Dic7311yescharacteristic
448C22×C4C22×Dic7311yescharacteristic
449C22×C4C22×Dic7311yescharacteristic
450C22×C4C22×Dic7311yescharacteristic
451C22×C4C22×Dic7311yescharacteristic
452C22×C4C22×Dic7311yescharacteristic
453C22×C4C22×Dic7311yescharacteristic
454C22×C4C22×Dic7311yescharacteristic
455C22×C4C22×Dic7311yescharacteristic
456C22×C4C22×Dic7311yescharacteristic
457C22×C4C22×Dic7311yescharacteristic
458C22×C4C23×D7311yescharacteristic
459C2×C8—732no—
460C2×C8—732no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8—1461no—
466C2×C8—1461no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8—1461no—
470C2×C8—1461no—
471C2×C8—1461no—
472C2×C8—1461no—
473C2×C8—1461no—
474C2×C8—1461no—
475C2×C8—1461no—
476C2×C8—1461no—
477C2×C8—1461no—
478C2×C8—1461no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42D4×D7312yes—
511C42#1192402712yes—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C23×Dic7311yescharacteristic
520Q8—44no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4D4×Dic7312yes—
561C2×C4D4×Dic7312yes—
562C2×C4#1455659812yes—
563C2×C4#1455659812yes—
564C2×C4C2×D4×D7311yescharacteristic
565C2×C4C2×#1192402711yescharacteristic
566C2×C4#1455663711yescharacteristic
567C2×C4#1455663811yescharacteristic
568C2×C4#1455663911yescharacteristic
569C2×C4#1455663911yescharacteristic
570C8—2921no—
571C8—2921no—
572C8—2921no—
573C8—2921no—
574C8—2921no—
575C8—2921no—
576C8—1462no—
577C8—1462no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×D4×Dic7311yescharacteristic
586C22#1798906511yescharacteristic
587C22#1798907011yescharacteristic
588C22C2×#1455659811yescharacteristic
589C22C2×#1455659811yescharacteristic
590C22#1798935411yescharacteristic
591C22#1798935411yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4#1798916011yescharacteristic
606C4#1798916711yescharacteristic
607C4#1798919711yescharacteristic
608C4#1798921011yescharacteristic
609C2—81no—
610C2#2261261511yescharacteristic
611C2#2261865811yescharacteristic
612C2#2261867511yescharacteristic
613C2#2261902611yescharacteristic
614C2#2261902611yescharacteristic
615C2#2261909111yescharacteristic
616C2#2261910111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2396C2
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenter#2396D73
hypocenterC73#22107
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2396

Complements

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

NH ≅ G/Ntype
1. C2×#17988718C2semidirect
3. #22610868C2semidirect
4. #22610655C2semidirect
5. #22610650C2semidirect
6. #22610650C2semidirect
11. #22610497C2semidirect
12. #22610490C2semidirect
14. #22609806C2semidirect
324. C73#22107semidirect

Maximal subgroups

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

subgroupindex
C2×#179887182
C2×#179886482
#226108682
#226106552
#226106502
#226105462
#226105392
#226104972
#226104902
#226099152
#226098062
C73×#23962
#2210773