Finite Group Databasebeta

← #34027788

Subgroups — #34027788

Order 18688.

860 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#10596833C211yesmaximal, characteristic
2C2×#17989611C211yesmaximal, characteristic, complemented
3#22626030C211yesmaximal, characteristic, complemented
4#22626005C211yesmaximal, characteristic, complemented
5#22626004C211yesmaximal, characteristic, complemented
6#22625985C211yesmaximal, characteristic, complemented
7#22625984C211yesmaximal, characteristic, complemented
8#22625908C211yesmaximal, characteristic
9#22625875C211yesmaximal, characteristic, complemented
10#22625875C211yesmaximal, characteristic, complemented
11#22625731C211yesmaximal, characteristic, complemented
12#22625673C211yesmaximal, characteristic, complemented
13C22⋊C4×#10596833C211yesmaximal, characteristic, complemented
14#22625597C211yesmaximal, characteristic, complemented
15#22613187C211yesmaximal, characteristic
16C22×#11924037C2211yescharacteristic
17C23×#10596833C2211yescharacteristic
18C23×#10596833C2211yescharacteristic
19D4×#10596833—24no—
20#17989611—24no—
21C2×#14556658C2211yescharacteristic
22C2×#14556658C2211yescharacteristic
23C2×#14556658C2211yescharacteristic
24C2×C4⋊#10596833C2211yescharacteristic
25C2×C4⋊#10596833C2211yescharacteristic
26C2×C22⋊#10596833C2211yescharacteristic
27C2×C22⋊#10596833C2211yescharacteristic
28C2×C22⋊#10596833C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×C22⋊#10596833C2211yescharacteristic
31C2×#14556646C2211yescharacteristic
32C2×#14556646C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
34C2×C4×#10596833C2211yescharacteristic
35C2×C4×#10596833C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44#17989453C2211yescharacteristic
45#17989453C2211yescharacteristic
46C2×D4×Dic73C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48#17988529C411yescharacteristic
49#17988523C411yescharacteristic
50#17988520C411yescharacteristic
51#17988515C411yescharacteristic
52#17988515C411yescharacteristic
53#17988512C411yescharacteristic
54#17988501C411yescharacteristic
55C4⋊C4×Dic73C2211yescharacteristic
56#17988438C2211yescharacteristic
57C22⋊C4×Dic73C2211yescharacteristic
58C22⋊C4×Dic73C2211yescharacteristic
59C22⋊C4×Dic73C2211yescharacteristic
60#394×C73C411yescharacteristic
61C2×#11924037—22no—
62C2×#11924037—22no—
63C2×#11924037—41no—
64C22×#10596833—22no—
65C22×#10596833—22no—
66C22×#10596833—22no—
67C22×#10596833—22no—
68C22×#10596833—41no—
69C22×#10596833—41no—
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73C22×#10596833C2311yescharacteristic
74C22×#10596833C2311yescharacteristic
75C22×#10596833C2311yescharacteristic
76C22×#10596833C2311yescharacteristic
77C22×#10596833C2311yescharacteristic
78#14556658—22no—
79#14556658—22no—
80#14556658—41no—
81C4⋊#10596833—22no—
82C4⋊#10596833—22no—
83C22⋊#10596833—22no—
84C22⋊#10596833—22no—
85C22⋊#10596833—22no—
86C22⋊#10596833—41no—
87C22⋊#10596833D414yes—
88#14556646—22no—
89#14556646—22no—
90C4×#10596833—22no—
91C4×#10596833—22no—
92C4×#10596833—41no—
93C23×Dic73C2311yescharacteristic
94C23×Dic73C2311yescharacteristic
95D4×Dic73—22no—
96D4×Dic73—22no—
97#14556547—22no—
98#14556547—22no—
99C2×C4⋊Dic73C2×C411yescharacteristic
100C2×C4⋊Dic73C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×C22⋊Dic73C2×C411yescharacteristic
106C2×C22⋊Dic73C2×C411yescharacteristic
107C2×C22⋊Dic73C2×C411yescharacteristic
108C2×C22⋊Dic73C2×C411yescharacteristic
109C2×C22⋊Dic73C2×C411yescharacteristic
110C2×C22⋊Dic73C2×C411yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C2×C4×Dic73C2311yescharacteristic
114C2×C4×Dic73C2311yescharacteristic
115C2×C4×Dic73C2311yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120#14556498C2×C411yescharacteristic
121#14556498C2×C411yescharacteristic
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125C22×D4×C73C2×C411yescharacteristic
126C2×C4⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129C2×C22⋊C4×C73C2×C411yescharacteristic
130C2×C22⋊C4×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#11924037—44no—
133C2×#10596833—21no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—44no—
154C2×#10596833—44no—
155C2×#10596833C2×D412yes—
156C2×#10596833C2×D412yes—
157C2×#10596833#4112yes—
158C2×#10596833#4112yes—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C22×Dic73C22×C411yescharacteristic
173C22×Dic73C22×C411yescharacteristic
174C22×Dic73C22×C411yescharacteristic
175C22×Dic73C22×C411yescharacteristic
176C22×Dic73C2×D412yes—
177C22×Dic73#4112yes—
178C22×Dic73C2411yescharacteristic
179C4⋊Dic73—22no—
180C4⋊Dic73—41no—
181#11924007—22no—
182#11924007—22no—
183#11924007—22no—
184#11924007—22no—
185C22⋊Dic73—22no—
186C22⋊Dic73—22no—
187C22⋊Dic73—22no—
188C22⋊Dic73—22no—
189C22⋊Dic73—22no—
190C22⋊Dic73—22no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C24×C73C22×C411yescharacteristic
202C24×C73C22×C411yescharacteristic
203C2×D4×C73—22no—
204C2×D4×C73—22no—
205C2×D4×C73—22no—
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C4⋊C4×C73—22no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—41no—
215C22⋊C4×C73—41no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73C4×D412yes—
229C23×C73#13112yes—
230C23×C73C23×C411yescharacteristic
231D4×C73—28no—
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#13112yes—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—21no—
251C2×Dic73—22no—
252C2×Dic73—22no—
253C2×Dic73—22no—
254C2×Dic73—22no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—21no—
261C2×Dic73—21no—
262C2×Dic73—21no—
263C2×Dic73—21no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—21no—
269C2×Dic73—21no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—41no—
274C2×Dic73C4×D412yes—
275C2×Dic73#13112yes—
276C2×Dic73C22×D411yescharacteristic
277C2×Dic73C2×#4111yescharacteristic
278C2×Dic73C2×#4111yescharacteristic
279C2×Dic73C2×#4111yescharacteristic
280C2×Dic73H(5,𝔽2)11yescharacteristic
281C2×Dic732−1+411yescharacteristic
282#10596833—22no—
283#10596833—22no—
284#10596833—22no—
285#10596833—22no—
286#10596833—41no—
287#10596833—41no—
288#10596833—41no—
289#10596833—41no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—22no—
295C22×C73—22no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73C2×C4×D411yescharacteristic
305C22×C73C4×#4111yescharacteristic
306C22×C73#52011yescharacteristic
307C22×C73C2×#13111yescharacteristic
308C22×C73C2×#13111yescharacteristic
309C22×C73C2×#13111yescharacteristic
310C22×C73#56811yescharacteristic
311C4×C73—22no—
312C4×C73—41no—
313C4×C73—41no—
314C4×C73—41no—
315C4×C73—41no—
316Dic73—22no—
317Dic73—22no—
318Dic73—41no—
319Dic73—41no—
320Dic73—41no—
321Dic73—41no—
322Dic73—41no—
323Dic73#54611yescharacteristic
324Dic73#54711yescharacteristic
325Dic73#55111yescharacteristic
326Dic73#55211yescharacteristic
327#22901—731nomaximal, Sylow
328C2×C73—42no—
329C2×C73—42no—
330C2×C73#235911yescharacteristic
331C2×C73#292911yescharacteristic
332C2×C73#293511yescharacteristic
333C2×C73#296611yescharacteristic
334C2×C73#296911yescharacteristic
335C2×C73#299211yescharacteristic
336C2×C73#299411yescharacteristic
337C2×C8×D4—731no—
338C2×#433—731no—
339#2395—731no—
340#1939—731no—
341#1924—731no—
342#1924—731no—
343#1916—731no—
344#1916—731no—
345#1870—731no—
346#1850—731no—
347#1850—731no—
348#1771—731no—
349#1753—731no—
350C8×C22⋊C4—731no—
351#1729—731no—
352C73#2290111yescharacteristic, complemented, Sylow
353C22×M16—731no—
354C23×C8—731no—
355C23×C8—731no—
356C2×C4×D4—731no—
357C2×#117—731no—
358C8×D4—1464no—
359#433—1464no—
360C2×C4⋊C8—731no—
361C2×C4⋊C8—731no—
362C2×C4⋊C8—731no—
363C2×C4⋊C8—731no—
364C2×C4⋊C8—731no—
365C2×C22⋊C8—731no—
366C2×C22⋊C8—731no—
367C2×C22⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×#97—731no—
371C2×#97—731no—
372C2×C4×C8—731no—
373C2×C4×C8—731no—
374C2×C4×C8—731no—
375#400—731no—
376#399—731no—
377#398—731no—
378#397—731no—
379#397—731no—
380#397—731no—
381#394—731no—
382#394#6440811yescharacteristic
383C4×C4⋊C4—731no—
384C4×C4⋊C4—731no—
385C4×C22⋊C4—731no—
386C4×C22⋊C4—731no—
387C4×C22⋊C4—731no—
388#336—731no—
389#336—731no—
390#336—731no—
391#336—731no—
392#336—731no—
393#336—731no—
394#336—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398C22×D4C2×#6440811yescharacteristic
399C23×C4—731no—
400C23×C4—731no—
401C2×M16—2921no—
402C2×M16—1462no—
403C2×M16—1462no—
404C22×C8—2921no—
405C22×C8—2921no—
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411C22×C8—731no—
412C22×C8—731no—
413C22×C8—731no—
414C22×C8—1462no—
415C22×C8—1462no—
416C22×C8—1462no—
417C22×C8—1462no—
418C4×D4—1462no—
419C4×D4—1462no—
420#117—1462no—
421#117—1462no—
422C2×C4⋊C4—731no—
423C2×C4⋊C4—731no—
424C2×C4⋊C4—731no—
425C2×C4⋊C4—731no—
426C2×C4⋊C4—731no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4C2×#6440811yescharacteristic
429C2×C22⋊C4—731no—
430C2×C22⋊C4—731no—
431C2×C22⋊C4—731no—
432C2×C22⋊C4—731no—
433C2×C22⋊C4—731no—
434C2×C22⋊C4—731no—
435C2×C22⋊C4C2×#6440811yescharacteristic
436C2×C22⋊C4C2×#6440811yescharacteristic
437C2×C22⋊C4C2×#6440811yescharacteristic
438C2×C22⋊C4C2×#6440811yescharacteristic
439C2×C42—731no—
440C2×C42—731no—
441C2×C42—731no—
442C2×C42—731no—
443C2×C42—731no—
444C4⋊C8—2921no—
445C4⋊C8—1462no—
446C4⋊C8—1462no—
447C4⋊C8—1462no—
448C4⋊C8—1462no—
449C22⋊C8—2921no—
450C22⋊C8—734no—
451C22⋊C8—1462no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454#97—1462no—
455#97—1462no—
456C4×C8—2921no—
457C4×C8—1462no—
458C4×C8—1462no—
459#95—731no—
460#95—731no—
461#95—731no—
462#95—731no—
463#95—731no—
464#95—731no—
465#95—731no—
466#95—731no—
467#95—731no—
468#95C2×#6440811yescharacteristic
469C24C22×#6440811yescharacteristic
470C24C22×#6440811yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C22×C4—731no—
475C22×C4—731no—
476C22×C4—731no—
477C22×C4—732no—
478C22×C4—732no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—731no—
482C22×C4—731no—
483C22×C4—731no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4—1461no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C22×C4C22×#6440811yescharacteristic
495C22×C4C22×#6440811yescharacteristic
496C22×C4C22×#6440811yescharacteristic
497C22×C4C22×#6440811yescharacteristic
498C22×C4C22×#6440811yescharacteristic
499M16—2924no—
500C2×C8—2924no—
501C2×C8—2924no—
502C2×C8—732no—
503C2×C8—732no—
504C2×C8—732no—
505C2×C8—732no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8—1461no—
520C2×C8—1461no—
521C2×C8—1461no—
522C2×C8—1461no—
523C2×C8—1461no—
524C2×C8—1461no—
525C2×C8—1461no—
526C4⋊C4—22no—
527C4⋊C4—2921no—
528C4⋊C4—1462no—
529C4⋊C4—1462no—
530C4⋊C4—1462no—
531C4⋊C4—1462no—
532C4⋊C4—1462no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—1462no—
538C22⋊C4—1462no—
539C22⋊C4—1462no—
540C22⋊C4—1462no—
541C22⋊C4—1462no—
542C22⋊C4—1462no—
543C42—1461no—
544C42—1461no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42—1461no—
552C42—1461no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23D4×#6440812yes—
566C23#1455667812yes—
567C23C23×#6440811yescharacteristic
568D4—28no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—2921no—
586C2×C4—2921no—
587C2×C4—731no—
588C2×C4—731no—
589C2×C4—731no—
590C2×C4—731no—
591C2×C4—731no—
592C2×C4—731no—
593C2×C4—732no—
594C2×C4—732no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4—1461no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1462no—
611C2×C4—1462no—
612C2×C4—1462no—
613C2×C4—1462no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4#1455667812yes—
619C8—2921no—
620C8—2921no—
621C8—2921no—
622C8—2921no—
623C8—1462no—
624C8—1462no—
625C8—1462no—
626C8—1462no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×D4×#6440811yescharacteristic
642C22#41×#6440811yescharacteristic
643C22#1798965611yescharacteristic
644C22C2×#1455667811yescharacteristic
645C22C2×#1455667811yescharacteristic
646C22D73⋊#13111yescharacteristic
647C22#1798966511yescharacteristic
648C4—22no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—2921no—
654C4—2921no—
655C4—2921no—
656C4—2921no—
657C4—2921no—
658C4—731no—
659C4—731no—
660C4—731no—
661C4—731no—
662C4—1462no—
663C4—1462no—
664C2—42no—
665C2—42no—
666C2#2262645411yescharacteristic
667C2#2262664611yescharacteristic
668C2#2262667511yescharacteristic
669C2#2262674611yescharacteristic
670C2#2262676211yescharacteristic
671C2#2262686711yescharacteristic
672C2#2262688111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#394×C73C4
prime radicalC22×D4×C73C2×C4
cosocleC22×Dic73C24
hypercenter#394#64408
hypocenterC73#22901
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#17989611C2semidirect
3. #22626030C2semidirect
4. #22626005C2semidirect
5. #22626004C2semidirect
6. #22625985C2semidirect
7. #22625984C2semidirect
9. #22625875C2semidirect
10. #22625875C2semidirect
11. #22625731C2semidirect
12. #22625673C2semidirect
13. C22⋊C4×#10596833C2semidirect
14. #22625597C2semidirect
352. C73#22901semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#105968332
C2×#179896112
#226260302
#226260052
#226260042
#226259852
#226259842
#226259082
#226258752
#226257312
#226256732
C22⋊C4×#105968332
#226255972
#226131872
#2290173