Finite Group Databasebeta

← #32992496

Subgroups — #32992496

Order 18688.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556571C211yesmaximal, characteristic
2C22×#14556516C211yesmaximal, characteristic, complemented
3C22×#14556514C211yesmaximal, characteristic, complemented
4C22×#14556503C211yesmaximal, characteristic
5C2×#17988444C211yesmaximal, characteristic
6C2×#17988349C211yesmaximal, characteristic, complemented
7C2×#340×C73C211yesmaximal, characteristic, complemented
8C23×Dic146C2211yescharacteristic
9C23×C4×D73C2211yescharacteristic
10C23×#10596831C2211yescharacteristic
11C2×#14556571—22no—
12C2×#14556571—22no—
13C2×#14556571—22no—
14C2×#14556571—22no—
15C2×#14556571—22no—
16C2×#14556571C414yescomplemented
17C22×C4⋊Dic73—21no—
18C22×C4⋊Dic73C2211yescharacteristic
19C22×#11924005—21no—
20C22×#11924005—21no—
21C2×#14556516—22no—
22C2×#14556516—22no—
23C2×#14556516—22no—
24C2×#14556514—22no—
25C2×#14556514—22no—
26C2×#14556514—22no—
27C2×#14556503—22no—
28C2×#14556503—22no—
29C2×#14556503—22no—
30#17988444—22no—
31#17988444—22no—
32C2×#14556498—21no—
33#17988349—22no—
34C23×C8×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36C22×C4⋊C4×C73C2211yescharacteristic
37#340×C73—22no—
38C24×D73D411yescharacteristic
39C22×Dic146—21no—
40C22×Dic146—21no—
41C22×Dic146—21no—
42C22×Dic146—21no—
43C22×Dic146—21no—
44C22×Dic146—21no—
45C22×Dic146—21no—
46C22×Dic146—21no—
47C22×Dic146—21no—
48C22×Dic146—21no—
49C22×Dic146—21no—
50C22×Dic146C2×C412yes—
51C22×Dic146D412yes—
52C22×Dic146D412yes—
53C23×Dic73—21no—
54C23×Dic73—21no—
55C23×Dic73D411yescharacteristic
56C22×C4×D73—21no—
57C22×C4×D73—21no—
58C22×C4×D73—21no—
59C22×C4×D73—21no—
60C22×C4×D73—21no—
61C22×C4×D73—21no—
62C22×C4×D73—21no—
63C22×C4×D73—21no—
64C22×C4×D73—21no—
65C22×C4×D73—21no—
66C22×C4×D73—21no—
67C22×C4×D73—21no—
68C22×C4×D73C2×C412yes—
69C22×C4×D73D412yes—
70C22×#10596831—21no—
71C22×#10596831—21no—
72C22×#10596831—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75C22×#10596831—21no—
76C22×#10596831D412yes—
77#14556571—28no—
78#14556571—28no—
79#14556571—28no—
80#14556571—28no—
81C2×C4⋊Dic73—24no—
82C2×C4⋊Dic73—24no—
83C2×C4⋊Dic73—24no—
84C2×C4⋊Dic73—21no—
85C2×C4⋊Dic73—21no—
86C2×C4⋊Dic73—21no—
87C2×C4⋊Dic73—21no—
88C2×C4⋊Dic73—21no—
89C2×C4⋊Dic73D412yes—
90C2×#11924005—24no—
91C2×#11924005—24no—
92C2×#11924005—24no—
93C2×#11924005—24no—
94C2×#11924005—42no—
95C2×#11924005—42no—
96#14556516—28no—
97#14556514—28no—
98#14556503—28no—
99#14556498—24no—
100C23×C4×C73—21no—
101C23×C4×C73—21no—
102C23×C4×C73C2311yescharacteristic
103C22×C8×C73—21no—
104C22×C8×C73—21no—
105C22×C8×C73—21no—
106C22×C8×C73—21no—
107C22×C8×C73—21no—
108C22×C8×C73—21no—
109C22×C8×C73D412yes—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73C2×C412yes—
119C2×C4⋊C4×C73D412yes—
120C2×C4⋊C4×C73D412yes—
121C2×C4⋊C4×C73D412yes—
122C23×D73—21no—
123C23×D73—21no—
124C23×D73—21no—
125C23×D73—21no—
126C23×D73—21no—
127C23×D73—21no—
128C23×D73—21no—
129C23×D73—21no—
130C23×D73—21no—
131C23×D73—21no—
132C23×D73—21no—
133C23×D73—21no—
134C23×D73C22⋊C412yes—
135C23×D73SD1612yes—
136C23×D73Q1612yes—
137C2×Dic146—22no—
138C2×Dic146—22no—
139C2×Dic146—22no—
140C2×Dic146—22no—
141C2×Dic146—22no—
142C2×Dic146—22no—
143C2×Dic146—22no—
144C2×Dic146—22no—
145C2×Dic146—22no—
146C2×Dic146—22no—
147C2×Dic146—22no—
148C2×Dic146—22no—
149C2×Dic146—22no—
150C2×Dic146—22no—
151C2×Dic146—22no—
152C2×Dic146—41no—
153C2×Dic146—41no—
154C2×Dic146—41no—
155C2×Dic146—41no—
156C2×Dic146—41no—
157C2×Dic146—41no—
158C2×Dic146—41no—
159C2×Dic146—41no—
160C2×Dic146—41no—
161C2×Dic146—41no—
162C2×Dic146—41no—
163C2×Dic146—41no—
164C2×Dic146C22⋊C414yescomplemented
165C22×Dic73—22no—
166C22×Dic73—21no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—22no—
175C22×Dic73—41no—
176C22×Dic73—41no—
177C22×Dic73—41no—
178C22×Dic73—41no—
179C22×Dic73—41no—
180C22×Dic73—41no—
181C22×Dic73—41no—
182C22×Dic73—41no—
183C22×Dic73—41no—
184C22×Dic73—41no—
185C22×Dic73C22⋊C412yes—
186C2×C4×D73—22no—
187C2×C4×D73—22no—
188C2×C4×D73—22no—
189C2×C4×D73—22no—
190C2×C4×D73—22no—
191C2×C4×D73—22no—
192C2×C4×D73—22no—
193C2×C4×D73—22no—
194C2×C4×D73—22no—
195C2×C4×D73—22no—
196C2×C4×D73—22no—
197C2×C4×D73—22no—
198C2×C4×D73—41no—
199C2×C4×D73—41no—
200C2×C4×D73—41no—
201C2×C4×D73—41no—
202C2×C4×D73—41no—
203C2×C4×D73—41no—
204C2×C4×D73—41no—
205C2×C4×D73—41no—
206C2×C4×D73—41no—
207C2×C4×D73—41no—
208C2×C4×D73—41no—
209C2×C4×D73—41no—
210C2×C4×D73—41no—
211C2×C4×D73—41no—
212C2×C4×D73—41no—
213C2×C4×D73—41no—
214C2×#10596831—22no—
215C2×#10596831—22no—
216C2×#10596831—22no—
217C2×#10596831—41no—
218C2×#10596831—41no—
219C2×#10596831—41no—
220C2×#10596831—41no—
221C4⋊Dic73—216no—
222C4⋊Dic73—22no—
223C4⋊Dic73—22no—
224C4⋊Dic73—41no—
225C4⋊Dic73—41no—
226#11924005—216no—
227#11924005—48no—
228C24×C73C2×D411yescharacteristic
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—41no—
234C22×C4×C73—41no—
235C22×C4×C73—41no—
236C22×C4×C73—41no—
237C22×C4×C73—41no—
238C22×C4×C73—41no—
239C22×C4×C73—41no—
240C22×C4×C73—41no—
241C22×C4×C73—41no—
242C22×C4×C73—41no—
243C22×C4×C73C22×C411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D411yescharacteristic
247C22×C4×C73C2×D411yescharacteristic
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D411yescharacteristic
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73#4111yescharacteristic
254C22×C4×C73#4111yescharacteristic
255C22×C4×C73#4111yescharacteristic
256C22×C4×C73#4111yescharacteristic
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73—22no—
260C2×C8×C73—41no—
261C2×C8×C73—41no—
262C2×C8×C73—41no—
263C2×C8×C73—41no—
264C4⋊C4×C73—22no—
265C4⋊C4×C73—22no—
266C4⋊C4×C73—22no—
267C4⋊C4×C73—22no—
268C4⋊C4×C73—22no—
269C4⋊C4×C73—41no—
270C4⋊C4×C73—41no—
271C4⋊C4×C73C22⋊C414yescomplemented
272C23×C73C2×C22⋊C411yescharacteristic
273C23×C73#12011yescharacteristic
274C23×C73#12011yescharacteristic
275C23×C73#12011yescharacteristic
276C23×C73#12111yescharacteristic
277C23×C73#12111yescharacteristic
278C23×C73#12311yescharacteristic
279C23×C73C2×SD1611yescharacteristic
280C23×C73C2×Q1611yescharacteristic
281C23×C73#13511yescharacteristic
282C23×C73#13511yescharacteristic
283C23×C73AGL(1,ℤ/8)11yescharacteristic
284C23×C73#13711yescharacteristic
285C23×C73#13711yescharacteristic
286C23×C73#13711yescharacteristic
287C22×D73—22no—
288C22×D73—22no—
289C22×D73—22no—
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—22no—
293C22×D73—22no—
294C22×D73—22no—
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—22no—
298C22×D73—22no—
299C22×D73—22no—
300C22×D73—22no—
301C22×D73—22no—
302C22×D73—22no—
303C22×D73—22no—
304C22×D73—22no—
305C22×D73—41no—
306C22×D73—41no—
307C22×D73—41no—
308C22×D73—41no—
309C22×D73—41no—
310C22×D73—41no—
311C22×D73—41no—
312C22×D73—41no—
313C22×D73—41no—
314C22×D73—41no—
315C22×D73—41no—
316C22×D73—41no—
317C22×D73—41no—
318C22×D73—41no—
319C22×D73—41no—
320C22×D73—41no—
321C22×D73#10314yescomplemented
322C2×C4×C73—24no—
323C2×C4×C73—42no—
324C2×C4×C73—42no—
325C2×C4×C73—42no—
326C2×C4×C73—42no—
327C2×C4×C73—42no—
328C2×C4×C73—42no—
329C2×C4×C73—42no—
330C2×C4×C73—42no—
331C2×C4×C73—42no—
332C2×C4×C73—81no—
333C2×C4×C73—81no—
334C2×C4×C73—81no—
335C2×C4×C73—81no—
336C2×C4×C73C2×C22⋊C411yescharacteristic
337C2×C4×C73C2×C22⋊C411yescharacteristic
338C2×C4×C73C4×D411yescharacteristic
339C2×C4×C73C4×D411yescharacteristic
340C2×C4×C73C4×D411yescharacteristic
341C2×C4×C73C4×D411yescharacteristic
342C2×C4×C73#12011yescharacteristic
343C2×C4×C73#12011yescharacteristic
344C2×C4×C73#12011yescharacteristic
345C2×C4×C73#12011yescharacteristic
346C2×C4×C73#12011yescharacteristic
347C2×C4×C73#12111yescharacteristic
348C2×C4×C73#12111yescharacteristic
349C2×C4×C73#12111yescharacteristic
350C2×C4×C73#12111yescharacteristic
351C2×C4×C73#12111yescharacteristic
352C2×C4×C73#12111yescharacteristic
353C2×C4×C73#12111yescharacteristic
354C2×C4×C73#12111yescharacteristic
355C2×C4×C73#12111yescharacteristic
356C2×C4×C73#12111yescharacteristic
357C2×C4×C73#12311yescharacteristic
358C2×C4×C73#12311yescharacteristic
359C2×C4×C73#12311yescharacteristic
360C2×C4×C73#12411yescharacteristic
361C2×C4×C73#12411yescharacteristic
362C2×C4×C73#12711yescharacteristic
363C2×C4×C73#12711yescharacteristic
364C2×Dic73—24no—
365C2×Dic73—22no—
366C2×Dic73—22no—
367C2×Dic73—22no—
368C2×Dic73—42no—
369C2×Dic73—42no—
370C2×Dic73—41no—
371C2×Dic73—41no—
372C2×Dic73—42no—
373C2×Dic73—42no—
374C2×Dic73—41no—
375C2×Dic73—41no—
376C2×Dic73—42no—
377C2×Dic73—42no—
378C2×Dic73—42no—
379C2×Dic73—42no—
380C2×Dic73—42no—
381C2×Dic73—81no—
382C2×Dic73—81no—
383C2×Dic73—81no—
384C2×Dic73—81no—
385C4×D73—42no—
386C4×D73—42no—
387C4×D73—42no—
388C4×D73—42no—
389C4×D73—42no—
390C4×D73—42no—
391C4×D73—42no—
392C4×D73—42no—
393Dic146—24no—
394Dic146—24no—
395Dic146—42no—
396Dic146—42no—
397Dic146—42no—
398Dic146—42no—
399Dic146—42no—
400Dic146—42no—
401C8×C73—42no—
402#10596831—42no—
403C22×C73#37911yescharacteristic
404C22×C73#38611yescharacteristic
405C22×C73#38611yescharacteristic
406C22×C73#39211yescharacteristic
407C22×C73#39211yescharacteristic
408C22×C73#39411yescharacteristic
409C22×C73#39411yescharacteristic
410C22×C73C2×#10311yescharacteristic
411C22×C73#41611yescharacteristic
412C22×C73#41711yescharacteristic
413C22×C73#41911yescharacteristic
414C22×C73#44811yescharacteristic
415C22×C73#44811yescharacteristic
416C22×C73#44911yescharacteristic
417C22×C73#44911yescharacteristic
418C22×C73#45011yescharacteristic
419C22×C73#45111yescharacteristic
420C22×C73#45111yescharacteristic
421C22×C73#45111yescharacteristic
422C22×C73#45211yescharacteristic
423C22×C73#45211yescharacteristic
424C22×C73#45211yescharacteristic
425C22×C73#45211yescharacteristic
426C22×C73#46511yescharacteristic
427C22×C73#46511yescharacteristic
428C22×C73#46711yescharacteristic
429C22×C73#46711yescharacteristic
430C22×C73#46811yescharacteristic
431C22×C73#46811yescharacteristic
432C22×C73#47011yescharacteristic
433C22×C73#47011yescharacteristic
434C22×C73#48311yescharacteristic
435C22×C73#48411yescharacteristic
436C22×C73#48511yescharacteristic
437C22×C73#48511yescharacteristic
438C2×D73—24no—
439C2×D73—24no—
440C2×D73—24no—
441C2×D73—42no—
442C2×D73—42no—
443C2×D73—42no—
444C2×D73—42no—
445C2×D73—42no—
446C2×D73—42no—
447C2×D73—42no—
448C2×D73—42no—
449C2×D73—42no—
450C2×D73—42no—
451C2×D73—42no—
452C2×D73—42no—
453C4×C73—44no—
454C4×C73—82no—
455C4×C73#38611yescharacteristic
456C4×C73#38611yescharacteristic
457C4×C73#39011yescharacteristic
458C4×C73#39011yescharacteristic
459C4×C73#39211yescharacteristic
460C4×C73#39211yescharacteristic
461C4×C73#39411yescharacteristic
462C4×C73#39411yescharacteristic
463Dic73—44no—
464Dic73—42no—
465Dic73—82no—
466#10970—731nomaximal, Sylow
467C2×C73#143811yescharacteristic
468C2×C73#178711yescharacteristic
469C2×C73#178811yescharacteristic
470C2×C73#187211yescharacteristic
471C2×C73#187311yescharacteristic
472C2×C73#189211yescharacteristic
473C2×C73#189411yescharacteristic
474C2×C73#200011yescharacteristic
475C2×C73#200011yescharacteristic
476C2×C73#200111yescharacteristic
477C2×C73#200111yescharacteristic
478C2×C73#203511yescharacteristic
479C2×C73#203511yescharacteristic
480C2×C73#203611yescharacteristic
481C2×C73#203611yescharacteristic
482D73—44no—
483C22×C22⋊Q8—731no—
484C22×#103—731no—
485C22×#103—731no—
486C22×C22⋊C8—731no—
487C2×#380—731no—
488C2×#340—731no—
489C2×#340D7311yescharacteristic, complemented
490C73#1097011yescharacteristic, complemented, Sylow
491C23×Q8—731no—
492C24×C4—731no—
493C23×C8—731no—
494C23×C8C2×D7311yescharacteristic
495C2×C22⋊Q8—734no—
496C2×C22⋊Q8—1462no—
497C2×C22⋊Q8—1462no—
498C2×C22⋊Q8—1462no—
499C2×C22⋊Q8—1462no—
500C2×C22⋊Q8—1462no—
501C22×C4⋊C4—731no—
502C22×C4⋊C4—1461no—
503C22×C4⋊C4C2×D7311yescharacteristic
504C22×C4⋊C4C2×D7311yescharacteristic
505C22×C22⋊C4—1461no—
506C22×C22⋊C4—1461no—
507C2×#103—1462no—
508C2×#103—1462no—
509C2×#103—1462no—
510C2×#103—1462no—
511C2×#103—1462no—
512C2×#103—1462no—
513C2×C22⋊C8—1462no—
514C2×C22⋊C8—1462no—
515C2×C22⋊C8—1462no—
516#380—1462no—
517#380—1462no—
518C2×#95—1461no—
519#340—22no—
520#340—1462no—
521C25—731no—
522C22×Q8—732no—
523C22×Q8—732no—
524C22×Q8—732no—
525C22×Q8—1461no—
526C22×Q8—1461no—
527C22×Q8—1461no—
528C22×Q8—1461no—
529C22×Q8—1461no—
530C22×Q8—1461no—
531C22×Q8—1461no—
532C22×Q8—1461no—
533C22×Q8—1461no—
534C22×Q8—1461no—
535C22×Q8—1461no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—731no—
539C23×C4—732no—
540C23×C4—732no—
541C23×C4—1461no—
542C23×C4—1461no—
543C23×C4—1461no—
544C23×C4—1461no—
545C23×C4—1461no—
546C23×C4—1461no—
547C23×C4—1461no—
548C23×C4—1461no—
549C23×C4—1461no—
550C23×C4—1461no—
551C23×C4—1461no—
552C23×C4—1461no—
553C23×C4—1461no—
554C23×C4—1461no—
555C23×C4C22×D7311yescharacteristic
556C22×C8—21no—
557C22×C8—21no—
558C22×C8—21no—
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8—732no—
563C22×C8—1461no—
564C22×C8—1461no—
565C22×C8—1461no—
566C22×C8—1461no—
567C22×C8—1461no—
568C22×C8—1461no—
569C22×C8D29212yes—
570C22⋊Q8—1468no—
571C22⋊Q8—1468no—
572C22⋊Q8—1468no—
573C22⋊Q8—1468no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—732no—
583C2×C4⋊C4—1461no—
584C2×C4⋊C4—1461no—
585C2×C4⋊C4—1461no—
586C2×C4⋊C4—1461no—
587C2×C4⋊C4—1461no—
588C2×C4⋊C4—1464no—
589C2×C4⋊C4—1464no—
590C2×C4⋊C4—1464no—
591C2×C4⋊C4C4×D7312yes—
592C2×C4⋊C4D29212yes—
593C2×C4⋊C4D29212yes—
594C2×C4⋊C4C22⋊D7312yes—
595C2×C22⋊C4—2922no—
596C2×C22⋊C4—2922no—
597C2×C22⋊C4—1464no—
598C2×C22⋊C4—1464no—
599C2×C22⋊C4—1464no—
600C2×C22⋊C4—1464no—
601#103—1468no—
602#103—1468no—
603C22⋊C8—1468no—
604#95—1464no—
605C24—732no—
606C24—732no—
607C24—732no—
608C24—1461no—
609C24—1461no—
610C24—1461no—
611C24—1461no—
612C24—1461no—
613C24—1461no—
614C24—1461no—
615C24—1461no—
616C24—1461no—
617C24—1461no—
618C24—1461no—
619C24—1461no—
620C24D4×D7311yescharacteristic
621C2×Q8—2921no—
622C2×Q8—2921no—
623C2×Q8—2921no—
624C2×Q8—2921no—
625C2×Q8—2921no—
626C2×Q8—2921no—
627C2×Q8—2921no—
628C2×Q8—2921no—
629C2×Q8—2921no—
630C2×Q8—2921no—
631C2×Q8—2921no—
632C2×Q8—2921no—
633C2×Q8—734no—
634C2×Q8—1462no—
635C2×Q8—1462no—
636C2×Q8—1462no—
637C2×Q8—1462no—
638C2×Q8—1462no—
639C2×Q8—1462no—
640C2×Q8—1462no—
641C2×Q8—1462no—
642C2×Q8—1462no—
643C2×Q8—1462no—
644C2×Q8—1462no—
645C2×Q8—1462no—
646C2×Q8—1462no—
647C2×Q8—1462no—
648C2×Q8—1462no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—2921no—
664C22×C4—2921no—
665C22×C4—2921no—
666C22×C4—2921no—
667C22×C4—2921no—
668C22×C4—2921no—
669C22×C4—2921no—
670C22×C4—2921no—
671C22×C4—2921no—
672C22×C4—2921no—
673C22×C4—2921no—
674C22×C4—2921no—
675C22×C4—2921no—
676C22×C4—2921no—
677C22×C4—2921no—
678C22×C4—2921no—
679C22×C4—2921no—
680C22×C4—2921no—
681C22×C4—2921no—
682C22×C4—2921no—
683C22×C4—2921no—
684C22×C4—2921no—
685C22×C4—2921no—
686C22×C4—2921no—
687C22×C4—2921no—
688C22×C4—2921no—
689C22×C4—732no—
690C22×C4—1462no—
691C22×C4—1462no—
692C22×C4—1462no—
693C22×C4—1461no—
694C22×C4—1461no—
695C22×C4—1462no—
696C22×C4—1461no—
697C22×C4—1461no—
698C22×C4—1461no—
699C22×C4—1461no—
700C22×C4—1462no—
701C22×C4—1462no—
702C22×C4—1462no—
703C22×C4—1462no—
704C22×C4—1462no—
705C22×C4—1462no—
706C22×C4—1462no—
707C22×C4—1462no—
708C22×C4—1462no—
709C22×C4—1462no—
710C22×C4—1462no—
711C22×C4—1462no—
712C22×C4C2×C4×D7311yescharacteristic
713C22×C4D4×D7311yescharacteristic
714C22×C4D4×D7311yescharacteristic
715C22×C4D4×D7311yescharacteristic
716C22×C4D4×D7311yescharacteristic
717C22×C4D4×D7311yescharacteristic
718C22×C4C2×C22⋊D7311yescharacteristic
719C22×C4C2×D29211yescharacteristic
720C22×C4C2×D29211yescharacteristic
721C22×C4C2×D29211yescharacteristic
722C22×C4#1192402811yescharacteristic
723C22×C4#1192402811yescharacteristic
724C22×C4#1192402911yescharacteristic
725C22×C4#1192402911yescharacteristic
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—2921no—
734C2×C8—2921no—
735C2×C8—2921no—
736C2×C8—2921no—
737C2×C8—1462no—
738C2×C8—1462no—
739C2×C8—1462no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—2921no—
748C4⋊C4—2921no—
749C4⋊C4—14616no—
750C4⋊C4—1462no—
751C4⋊C4—1462no—
752C4⋊C4#1192400514yescomplemented
753C22⋊C4—2928no—
754C22⋊C4—14616no—
755C23—2921no—
756C23—2921no—
757C23—2921no—
758C23—2921no—
759C23—2921no—
760C23—2921no—
761C23—2921no—
762C23—2921no—
763C23—2921no—
764C23—2921no—
765C23—2921no—
766C23—2921no—
767C23—2921no—
768C23—2921no—
769C23—2921no—
770C23—2921no—
771C23—734no—
772C23—1462no—
773C23—1462no—
774C23—1462no—
775C23—1462no—
776C23—1462no—
777C23—1462no—
778C23—1462no—
779C23—1462no—
780C23—1462no—
781C23—1462no—
782C23—1462no—
783C23—1462no—
784C23—1462no—
785C23—1462no—
786C23—1462no—
787C23—1462no—
788C23—1462no—
789C23—1462no—
790C23C22⋊C4×D7311yescharacteristic
791C23#1455655911yescharacteristic
792C23#1455656111yescharacteristic
793C23#1455656111yescharacteristic
794C23#1455656411yescharacteristic
795C23#1455656611yescharacteristic
796C23#1455657611yescharacteristic
797C23SD16×D7311yescharacteristic
798C23Q16×D7311yescharacteristic
799C23#1455661011yescharacteristic
800C23#1455661211yescharacteristic
801C23#1455661511yescharacteristic
802C23#1455662011yescharacteristic
803C23#1455662011yescharacteristic
804C23#1455662311yescharacteristic
805Q8—2922no—
806Q8—2922no—
807Q8—2922no—
808Q8—2922no—
809Q8—2922no—
810Q8—2922no—
811Q8—1464no—
812Q8—1464no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—2922no—
828C2×C4—2922no—
829C2×C4—2921no—
830C2×C4—2922no—
831C2×C4—2921no—
832C2×C4—2922no—
833C2×C4—2921no—
834C2×C4—2922no—
835C2×C4—2921no—
836C2×C4—2922no—
837C2×C4—2922no—
838C2×C4—2922no—
839C2×C4—2922no—
840C2×C4—2922no—
841C2×C4—2922no—
842C2×C4—2922no—
843C2×C4—2922no—
844C2×C4—2922no—
845C2×C4—2922no—
846C2×C4—2922no—
847C2×C4—2922no—
848C2×C4—5841no—
849C2×C4—5841no—
850C2×C4—5841no—
851C2×C4—5841no—
852C2×C4—1464no—
853C2×C4—1462no—
854C2×C4—1462no—
855C2×C4—1462no—
856C2×C4C22⋊C4×D7311yescharacteristic
857C2×C4C2×#1192400511yescharacteristic
858C2×C4#1455655311yescharacteristic
859C2×C4#1455655311yescharacteristic
860C2×C4C4×D29211yescharacteristic
861C2×C4C4×D29211yescharacteristic
862C2×C4#1455655911yescharacteristic
863C2×C4#1455656111yescharacteristic
864C2×C4#1455656111yescharacteristic
865C2×C4#1455656111yescharacteristic
866C2×C4#1455656111yescharacteristic
867C2×C4#1455656411yescharacteristic
868C2×C4#1455656411yescharacteristic
869C2×C4#1455656411yescharacteristic
870C2×C4#1455656511yescharacteristic
871C2×C4#1455656511yescharacteristic
872C2×C4#1455656611yescharacteristic
873C2×C4#1455656611yescharacteristic
874C2×C4#1455656611yescharacteristic
875C2×C4#1455656611yescharacteristic
876C2×C4#1455656611yescharacteristic
877C2×C4#1455657611yescharacteristic
878C2×C4#1455657611yescharacteristic
879C2×C4#1455657611yescharacteristic
880C2×C4#1455657911yescharacteristic
881C2×C4#1455658011yescharacteristic
882C2×C4#1455658711yescharacteristic
883C2×C4#1455658811yescharacteristic
884C8—42no—
885C8—2922no—
886C22—2922no—
887C22—2922no—
888C22—2922no—
889C22—2922no—
890C22—2922no—
891C22—2922no—
892C22—2922no—
893C22—2922no—
894C22—2922no—
895C22—2922no—
896C22—2922no—
897C22—2922no—
898C22—1464no—
899C22—1464no—
900C22—1464no—
901C22#1798844211yescharacteristic
902C22#1798846511yescharacteristic
903C22#1798846511yescharacteristic
904C22#1798849611yescharacteristic
905C22#1798849711yescharacteristic
906C22#1798850411yescharacteristic
907C22#1798850511yescharacteristic
908C22#103×D7311yescharacteristic
909C22#1798858011yescharacteristic
910C22#1798858511yescharacteristic
911C22#1798859411yescharacteristic
912C22#1798872411yescharacteristic
913C22#1798872711yescharacteristic
914C22#1798872911yescharacteristic
915C22#1798873311yescharacteristic
916C22#1798873911yescharacteristic
917C22#1798874111yescharacteristic
918C22#1798874411yescharacteristic
919C22#1798874411yescharacteristic
920C22#1798874611yescharacteristic
921C22#1798875011yescharacteristic
922C22#1798875011yescharacteristic
923C22#1798875211yescharacteristic
924C22#1798881511yescharacteristic
925C22#1798881711yescharacteristic
926C22#1798882711yescharacteristic
927C22#1798882911yescharacteristic
928C22#1798883211yescharacteristic
929C22#1798883411yescharacteristic
930C22#1798884411yescharacteristic
931C22#1798884611yescharacteristic
932C22#1798891911yescharacteristic
933C22#1798892411yescharacteristic
934C22#1798893011yescharacteristic
935C22#1798893111yescharacteristic
936C4—44no—
937C4—82no—
938C4—2922no—
939C4—2924no—
940C4—5842no—
941C4#1798846511yescharacteristic
942C4#1798846511yescharacteristic
943C4#1798848811yescharacteristic
944C4#1798848911yescharacteristic
945C4#1798849611yescharacteristic
946C4#1798849711yescharacteristic
947C4#1798850411yescharacteristic
948C4#1798850511yescharacteristic
949C2—2924no—
950C2#2260817111yescharacteristic
951C2#2260986411yescharacteristic
952C2#2260986811yescharacteristic
953C2#2261023711yescharacteristic
954C2#2261024211yescharacteristic
955C2#2261035311yescharacteristic
956C2#2261036311yescharacteristic
957C2#2261093511yescharacteristic
958C2#2261093711yescharacteristic
959C2#2261094011yescharacteristic
960C2#2261094211yescharacteristic
961C2#2261112911yescharacteristic
962C2#2261113011yescharacteristic
963C2#2261113611yescharacteristic
964C2#2261113711yescharacteristic
subgroupG/H
centerC24D4×D73
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC2×#340×C73C2
socleC24×C73C2×D4
prime radicalC24×D73D4
cosocleC23×C4×C73C23
hypercenterC2×#340D73
hypocenterC73#10970
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14556516C2semidirect
3. C22×#14556514C2semidirect
6. C2×#17988349C2semidirect
7. C2×#340×C73C2semidirect
16. C2×#14556571C4semidirect
164. C2×Dic146C22⋊C4semidirect
271. C4⋊C4×C73C22⋊C4semidirect
321. C22×D73#103semidirect
489. C2×#340D73semidirect
490. C73#10970semidirect
752. C4⋊C4#11924005semidirect

Maximal subgroups

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

subgroupindex
C22×#145565712
C22×#145565162
C22×#145565142
C22×#145565032
C2×#179884442
C2×#179883492
C2×#340×C732
#1097073