Finite Group Databasebeta

← #33009011

Subgroups — #33009011

Order 18688.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988480C211yesmaximal, characteristic, complemented
2C2×#17988467C211yesmaximal, characteristic
3C2×#17988462C211yesmaximal, characteristic, complemented
4C2×#17988447C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
7#22608188C211yesmaximal, characteristic, complemented
8#22608180C211yesmaximal, characteristic, complemented
9#22608176C211yesmaximal, characteristic, complemented
10#22608172C211yesmaximal, characteristic
11#22608168C211yesmaximal, characteristic, complemented
12#22608165C211yesmaximal, characteristic, complemented
13#22608165C211yesmaximal, characteristic, complemented
14#22608156C211yesmaximal, characteristic, complemented
15C2×#386×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C4⋊Dic73C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C22×C22⋊Dic73C2211yescharacteristic
21C22×C22⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C4×Dic73C2211yescharacteristic
28C22×C4×Dic73C2211yescharacteristic
29C22×C4×Dic73C2211yescharacteristic
30#17988480—24no—
31#17988467—24no—
32#17988462—24no—
33#17988447—24no—
34C22⋊C4×Dic73—24no—
35C4×C22⋊Dic73—24no—
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C23×D4×C73C2211yescharacteristic
51C24×C4×C73C2211yescharacteristic
52C22×C22⋊C4×C73C2211yescharacteristic
53C22×C22⋊C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55#386×C73C418yescomplemented
56C2×#95×C73C2211yescharacteristic
57C2×#95×C73C2211yescharacteristic
58C23×Dic73—22no—
59C23×Dic73—22no—
60C23×Dic73—22no—
61C23×Dic73—22no—
62C23×Dic73—22no—
63C23×Dic73—41no—
64C23×Dic73—41no—
65C23×Dic73C2311yescharacteristic
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C23×Dic73C2311yescharacteristic
72C23×Dic73C2311yescharacteristic
73C2×C4⋊Dic73—22no—
74C2×C4⋊Dic73—22no—
75C2×C4⋊Dic73—22no—
76C2×C4⋊Dic73—22no—
77C2×C4⋊Dic73—22no—
78C2×C4⋊Dic73—22no—
79C2×C4⋊Dic73—22no—
80C2×C4⋊Dic73—41no—
81C2×C4⋊Dic73—41no—
82C2×C22⋊Dic73—22no—
83C2×C22⋊Dic73—22no—
84C2×C22⋊Dic73—22no—
85C2×C22⋊Dic73—22no—
86C2×C22⋊Dic73—22no—
87C2×C22⋊Dic73—22no—
88C2×C22⋊Dic73—22no—
89C2×C22⋊Dic73—22no—
90C2×C22⋊Dic73—22no—
91C2×C22⋊Dic73—22no—
92C2×C22⋊Dic73—22no—
93C2×C22⋊Dic73—22no—
94C2×C22⋊Dic73—22no—
95C2×C22⋊Dic73—22no—
96C2×C22⋊Dic73—22no—
97C2×C22⋊Dic73—22no—
98C2×C22⋊Dic73—41no—
99C2×C22⋊Dic73—41no—
100C2×C22⋊Dic73—41no—
101C2×C22⋊Dic73—41no—
102C2×C22⋊Dic73D414yes—
103C2×C4×Dic73—22no—
104C2×C4×Dic73—22no—
105C2×C4×Dic73—22no—
106C2×C4×Dic73—22no—
107C2×C4×Dic73—22no—
108C2×C4×Dic73—22no—
109C2×C4×Dic73—41no—
110C2×C4×Dic73—41no—
111C2×C4×Dic73—41no—
112#14556498—22no—
113#14556498—22no—
114#14556498—22no—
115#14556498—22no—
116#14556498—22no—
117#14556498—22no—
118#14556498—22no—
119#14556498—22no—
120#14556498—22no—
121#14556498—41no—
122#14556498—41no—
123#14556498—41no—
124#14556498D414yescomplemented
125#14556498D414yescomplemented
126C25×C73C2311yescharacteristic
127C25×C73C2311yescharacteristic
128C22×D4×C73—22no—
129C22×D4×C73—22no—
130C22×D4×C73—22no—
131C22×D4×C73—22no—
132C22×D4×C73—41no—
133C22×D4×C73—41no—
134C22×D4×C73C2×C414yes—
135C23×C4×C73—22no—
136C23×C4×C73—22no—
137C23×C4×C73—22no—
138C23×C4×C73—22no—
139C23×C4×C73—41no—
140C23×C4×C73—41no—
141C23×C4×C73C2×C414yescomplemented
142C23×C4×C73C2311yescharacteristic
143C23×C4×C73C2311yescharacteristic
144C23×C4×C73C2311yescharacteristic
145C23×C4×C73C2311yescharacteristic
146C23×C4×C73C2311yescharacteristic
147C2×C22⋊C4×C73—22no—
148C2×C22⋊C4×C73—22no—
149C2×C22⋊C4×C73—22no—
150C2×C22⋊C4×C73—22no—
151C2×C22⋊C4×C73—22no—
152C2×C22⋊C4×C73—22no—
153C2×C22⋊C4×C73C2×C414yes—
154C2×C22⋊C4×C73C2×C414yes—
155C2×C22⋊C4×C73C2×C414yescomplemented
156#95×C73C2×C414yescomplemented
157#95×C73C2×C414yescomplemented
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—28no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—44no—
208C22×Dic73—44no—
209C22×Dic73—44no—
210C22×Dic73—44no—
211C22×Dic73—44no—
212C22×Dic73—44no—
213C22×Dic73C2×D412yes—
214C22×Dic73C2×D412yes—
215C22×Dic73C2×D412yes—
216C22×Dic73C2×D412yes—
217C22×Dic73C2×D412yes—
218C22×Dic73C2×D412yes—
219C22×Dic73#4112yes—
220C22×Dic73#4112yes—
221C4⋊Dic73—44no—
222C4⋊Dic73—44no—
223C4⋊Dic73—44no—
224C22⋊Dic73—28no—
225C22⋊Dic73—28no—
226C22⋊Dic73—28no—
227C22⋊Dic73—44no—
228C22⋊Dic73—44no—
229C22⋊Dic73—44no—
230C22⋊Dic73—44no—
231C4×Dic73—44no—
232C4×Dic73—44no—
233C4×Dic73—44no—
234C24×C73—21no—
235C24×C73—21no—
236C24×C73—21no—
237C24×C73—21no—
238C24×C73—21no—
239C24×C73—21no—
240C24×C73—21no—
241C24×C73—21no—
242C24×C73—21no—
243C24×C73—21no—
244C24×C73—21no—
245C24×C73—21no—
246C24×C73—21no—
247C24×C73—21no—
248C24×C73—21no—
249C24×C73—21no—
250C24×C73—21no—
251C24×C73—21no—
252C24×C73—21no—
253C24×C73—21no—
254C24×C73—21no—
255C24×C73—21no—
256C24×C73—21no—
257C24×C73—21no—
258C24×C73C22×C412yes—
259C24×C73C22×C412yes—
260C24×C73C2×D412yes—
261C24×C73#4112yes—
262C24×C73#4112yes—
263C24×C73#4112yes—
264C24×C73C2411yescharacteristic
265C2×D4×C73—28no—
266C2×D4×C73—28no—
267C2×D4×C73—44no—
268C2×D4×C73—44no—
269C2×D4×C73—44no—
270C2×D4×C73—44no—
271C2×D4×C73—44no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
286C22×C4×C73—21no—
287C22×C4×C73—21no—
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—21no—
298C22×C4×C73—28no—
299C22×C4×C73—28no—
300C22×C4×C73—44no—
301C22×C4×C73—44no—
302C22×C4×C73—44no—
303C22×C4×C73—44no—
304C22×C4×C73—44no—
305C22×C4×C73C22×C412yes—
306C22×C4×C73C22×C412yes—
307C22×C4×C73C22×C412yes—
308C22×C4×C73C22×C412yes—
309C22×C4×C73C22×C412yes—
310C22×C4×C73C2×D412yes—
311C22×C4×C73C2×D412yes—
312C22×C4×C73#4112yes—
313C22×C4×C73#4112yes—
314C22⋊C4×C73—28no—
315C22⋊C4×C73—28no—
316C22⋊C4×C73—28no—
317C23×C73—22no—
318C23×C73—22no—
319C23×C73—22no—
320C23×C73—22no—
321C23×C73—22no—
322C23×C73—22no—
323C23×C73—22no—
324C23×C73—22no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—22no—
328C23×C73—22no—
329C23×C73—22no—
330C23×C73—22no—
331C23×C73—22no—
332C23×C73—22no—
333C23×C73—22no—
334C23×C73—22no—
335C23×C73—22no—
336C23×C73—22no—
337C23×C73—22no—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73—22no—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73—22no—
345C23×C73—22no—
346C23×C73—22no—
347C23×C73—22no—
348C23×C73—22no—
349C23×C73—22no—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—22no—
353C23×C73—41no—
354C23×C73—41no—
355C23×C73—41no—
356C23×C73—41no—
357C23×C73—41no—
358C23×C73—41no—
359C23×C73—41no—
360C23×C73—41no—
361C23×C73—41no—
362C23×C73—41no—
363C23×C73—41no—
364C23×C73—41no—
365C23×C73—41no—
366C23×C73—41no—
367C23×C73—41no—
368C23×C73—41no—
369C23×C73—41no—
370C23×C73—41no—
371C23×C73—41no—
372C23×C73—41no—
373C23×C73—41no—
374C23×C73—41no—
375C23×C73—41no—
376C23×C73—41no—
377C23×C73—41no—
378C23×C73—41no—
379C23×C73—41no—
380C23×C73—41no—
381C23×C73—41no—
382C23×C73—41no—
383C23×C73—41no—
384C23×C73—41no—
385C23×C73#11714yes—
386C23×C73C4×D414yes—
387C23×C73C23×C411yescharacteristic
388C23×C73C22×D411yescharacteristic
389C23×C73C22×D411yescharacteristic
390C23×C73C22×D411yescharacteristic
391C23×C73C2×#4111yescharacteristic
392C23×C73C2×#4111yescharacteristic
393C23×C73C2×#4111yescharacteristic
394C23×C73C2×#4111yescharacteristic
395C23×C73C2×#4111yescharacteristic
396C23×C73C2×#4111yescharacteristic
397C23×C73C2×#4111yescharacteristic
398C23×C73H(5,𝔽2)11yescharacteristic
399C23×C73H(5,𝔽2)11yescharacteristic
400C23×C73H(5,𝔽2)11yescharacteristic
401C23×C732−1+411yescharacteristic
402D4×C73—416no—
403C2×C4×C73—22no—
404C2×C4×C73—22no—
405C2×C4×C73—22no—
406C2×C4×C73—22no—
407C2×C4×C73—22no—
408C2×C4×C73—22no—
409C2×C4×C73—22no—
410C2×C4×C73—22no—
411C2×C4×C73—22no—
412C2×C4×C73—22no—
413C2×C4×C73—22no—
414C2×C4×C73—22no—
415C2×C4×C73—22no—
416C2×C4×C73—22no—
417C2×C4×C73—22no—
418C2×C4×C73—22no—
419C2×C4×C73—22no—
420C2×C4×C73—22no—
421C2×C4×C73—22no—
422C2×C4×C73—22no—
423C2×C4×C73—22no—
424C2×C4×C73—416no—
425C2×C4×C73—41no—
426C2×C4×C73—41no—
427C2×C4×C73—41no—
428C2×C4×C73—41no—
429C2×C4×C73—41no—
430C2×C4×C73—41no—
431C2×C4×C73—41no—
432C2×C4×C73—41no—
433C2×C4×C73—41no—
434C2×C4×C73—41no—
435C2×C4×C73—41no—
436C2×C4×C73—41no—
437C2×C4×C73C4×D414yes—
438C2×C4×C73C4×D414yes—
439C2×Dic73—22no—
440C2×Dic73—22no—
441C2×Dic73—22no—
442C2×Dic73—22no—
443C2×Dic73—22no—
444C2×Dic73—22no—
445C2×Dic73—22no—
446C2×Dic73—22no—
447C2×Dic73—22no—
448C2×Dic73—22no—
449C2×Dic73—22no—
450C2×Dic73—22no—
451C2×Dic73—22no—
452C2×Dic73—22no—
453C2×Dic73—22no—
454C2×Dic73—22no—
455C2×Dic73—22no—
456C2×Dic73—22no—
457C2×Dic73—22no—
458C2×Dic73—22no—
459C2×Dic73—22no—
460C2×Dic73—416no—
461C2×Dic73—41no—
462C2×Dic73—41no—
463C2×Dic73—41no—
464C2×Dic73—41no—
465C2×Dic73—41no—
466C2×Dic73—41no—
467C2×Dic73—41no—
468C2×Dic73—41no—
469C2×Dic73—41no—
470C2×Dic73—41no—
471C2×Dic73—41no—
472C2×Dic73—41no—
473C2×Dic73—41no—
474C2×Dic73—41no—
475C2×Dic73—41no—
476C2×Dic73—41no—
477C2×Dic73—41no—
478C2×Dic73—41no—
479C2×Dic73—41no—
480C2×Dic73—41no—
481C2×Dic73—41no—
482C2×Dic73—41no—
483C2×Dic73—41no—
484C2×Dic73—41no—
485C2×Dic73—41no—
486C2×Dic73—41no—
487C2×Dic73—41no—
488C2×Dic73—41no—
489C2×Dic73—41no—
490C2×Dic73—41no—
491C2×Dic73—41no—
492C2×Dic73—41no—
493C2×Dic73—41no—
494C2×Dic73—41no—
495C2×Dic73#12114yes—
496C22×C73—24no—
497C22×C73—24no—
498C22×C73—24no—
499C22×C73—24no—
500C22×C73—24no—
501C22×C73—24no—
502C22×C73—42no—
503C22×C73—42no—
504C22×C73—42no—
505C22×C73—42no—
506C22×C73—42no—
507C22×C73—42no—
508C22×C73—42no—
509C22×C73—42no—
510C22×C73—42no—
511C22×C73—42no—
512C22×C73—42no—
513C22×C73—42no—
514C22×C73—42no—
515C22×C73—42no—
516C22×C73—42no—
517C22×C73—42no—
518C22×C73—42no—
519C22×C73—42no—
520C22×C73—42no—
521C22×C73—42no—
522C22×C73—42no—
523C22×C73—42no—
524C22×C73—42no—
525C22×C73—42no—
526C22×C73C2×#11711yescharacteristic
527C22×C73C2×C4×D411yescharacteristic
528C22×C73C2×C4×D411yescharacteristic
529C22×C73C2×C4×D411yescharacteristic
530C22×C73C4×#4111yescharacteristic
531C22×C73#51811yescharacteristic
532C22×C73#52011yescharacteristic
533C22×C73C2×#12111yescharacteristic
534C22×C73#52511yescharacteristic
535C22×C73#52511yescharacteristic
536C22×C73#52511yescharacteristic
537C22×C73#52911yescharacteristic
538C22×C73#52911yescharacteristic
539C22×C73#52911yescharacteristic
540C22×C73#53211yescharacteristic
541C22×C73#53811yescharacteristic
542C22×C73#53911yescharacteristic
543C22×C73#54011yescharacteristic
544C22×C73#54211yescharacteristic
545C22×C73D4211yescharacteristic
546C22×C73D4211yescharacteristic
547C22×C73#54611yescharacteristic
548C22×C73#54611yescharacteristic
549C22×C73#54611yescharacteristic
550C22×C73#54611yescharacteristic
551C22×C73#54611yescharacteristic
552C22×C73#54711yescharacteristic
553C22×C73#54811yescharacteristic
554C22×C73#54811yescharacteristic
555C22×C73#55111yescharacteristic
556C22×C73#55111yescharacteristic
557C22×C73#55111yescharacteristic
558C22×C73#55211yescharacteristic
559C22×C73#55311yescharacteristic
560C22×C73#55311yescharacteristic
561C4×C73—24no—
562C4×C73—24no—
563C4×C73—42no—
564C4×C73—42no—
565C4×C73—42no—
566Dic73—24no—
567Dic73—42no—
568Dic73—42no—
569Dic73—42no—
570Dic73—42no—
571Dic73—42no—
572Dic73—81no—
573Dic73—81no—
574#13988—731nomaximal, Sylow
575C2×C73—44no—
576C2×C73—44no—
577C2×C73#229011yescharacteristic
578C2×C73C4×#12111yescharacteristic
579C2×C73#233511yescharacteristic
580C2×C73#234211yescharacteristic
581C2×C73#235211yescharacteristic
582C2×C73#235811yescharacteristic
583C2×C73#236111yescharacteristic
584C2×C73#242411yescharacteristic
585C2×C73#242711yescharacteristic
586C2×C73#245711yescharacteristic
587C2×C73#246311yescharacteristic
588C2×C73#246411yescharacteristic
589C2×C73#247711yescharacteristic
590C2×C73#255311yescharacteristic
591C2×C73#257811yescharacteristic
592C2×#388—731no—
593C2×#386—731no—
594C2×#386D7311yescharacteristic
595C2×#385—731no—
596C2×#380—731no—
597C2×C4×C22⋊C4—731no—
598C2×C4×C22⋊C4—731no—
599#1442—731no—
600#1440—731no—
601#1439—731no—
602#1438—731no—
603#1437—731no—
604#1436—731no—
605#1436—731no—
606#1434—731no—
607C73#1398811yescharacteristic, complemented, Sylow
608C23×D4C2×D7311yescharacteristic
609C24×C4—731no—
610C24×C4C2×D7311yescharacteristic
611C22×C4⋊C4—731no—
612C22×C4⋊C4—731no—
613C22×C4⋊C4—731no—
614C22×C22⋊C4—731no—
615C22×C22⋊C4—731no—
616C22×C22⋊C4—731no—
617C22×C22⋊C4—731no—
618C22×C22⋊C4—731no—
619C22×C22⋊C4—731no—
620C22×C22⋊C4—731no—
621C22×C22⋊C4C2×D7311yescharacteristic
622C22×C22⋊C4C2×D7311yescharacteristic
623C22×C22⋊C4C2×D7311yescharacteristic
624C22×C42—731no—
625C22×C42—731no—
626C22×C42—731no—
627#388—1464no—
628#386—1464no—
629#386Dic7318yescomplemented
630#385—1464no—
631#380—1464no—
632C4×C22⋊C4—1464no—
633C4×C22⋊C4—1464no—
634C2×#95—731no—
635C2×#95—731no—
636C2×#95—731no—
637C2×#95—731no—
638C2×#95—731no—
639C2×#95—731no—
640C2×#95—731no—
641C2×#95—731no—
642C2×#95—731no—
643C2×#95—731no—
644C2×#95—731no—
645C2×#95—731no—
646C2×#95—731no—
647C2×#95—731no—
648C2×#95C2×D7311yescharacteristic
649C2×#95C2×D7311yescharacteristic
650C25C22×D7311yescharacteristic
651C25C22×D7311yescharacteristic
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—41no—
657C22×D4—41no—
658C22×D4C2×Dic7314yes—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—2921no—
666C23×C4—2921no—
667C23×C4—731no—
668C23×C4—731no—
669C23×C4—731no—
670C23×C4—731no—
671C23×C4—731no—
672C23×C4—731no—
673C23×C4—731no—
674C23×C4—731no—
675C23×C4—1462no—
676C23×C4—1462no—
677C23×C4—1462no—
678C23×C4—1462no—
679C23×C4—1462no—
680C23×C4C2×Dic7314yescomplemented
681C23×C4C22×D7311yescharacteristic
682C23×C4C22×D7311yescharacteristic
683C23×C4C22×D7311yescharacteristic
684C23×C4C22×D7311yescharacteristic
685C23×C4C22×D7311yescharacteristic
686C2×C4⋊C4—2921no—
687C2×C4⋊C4—2921no—
688C2×C4⋊C4—1462no—
689C2×C4⋊C4—1462no—
690C2×C4⋊C4—1462no—
691C2×C4⋊C4—1462no—
692C2×C4⋊C4—1462no—
693C2×C4⋊C4—1462no—
694C2×C4⋊C4—1462no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—2921no—
702C2×C22⋊C4—2921no—
703C2×C22⋊C4—2921no—
704C2×C22⋊C4—2921no—
705C2×C22⋊C4—734no—
706C2×C22⋊C4—1462no—
707C2×C22⋊C4—1462no—
708C2×C22⋊C4—1462no—
709C2×C22⋊C4—1462no—
710C2×C22⋊C4—1462no—
711C2×C22⋊C4—1462no—
712C2×C22⋊C4—1462no—
713C2×C22⋊C4—1462no—
714C2×C22⋊C4—1462no—
715C2×C22⋊C4—1462no—
716C2×C22⋊C4—1462no—
717C2×C22⋊C4—1462no—
718C2×C22⋊C4—1462no—
719C2×C22⋊C4—1462no—
720C2×C22⋊C4—1462no—
721C2×C22⋊C4—1462no—
722C2×C22⋊C4C2×Dic7314yes—
723C2×C22⋊C4C2×Dic7314yes—
724C2×C22⋊C4C2×Dic7314yescomplemented
725C2×C42—2921no—
726C2×C42—2921no—
727C2×C42—2921no—
728C2×C42—1462no—
729C2×C42—1462no—
730C2×C42—1462no—
731C2×C42—1462no—
732C2×C42—1462no—
733C2×C42—1462no—
734#95—2921no—
735#95—2921no—
736#95—2921no—
737#95—734no—
738#95—734no—
739#95—1462no—
740#95—1462no—
741#95—1462no—
742#95—1462no—
743#95—1462no—
744#95—1462no—
745#95—1462no—
746#95—1462no—
747#95—1462no—
748#95C2×Dic7314yescomplemented
749#95C2×Dic7314yescomplemented
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24C22×Dic7312yes—
775C24C22×Dic7312yes—
776C24D4×D7312yes—
777C24#1192402712yes—
778C24#1192402812yes—
779C24#1192402812yes—
780C24C23×D7311yescharacteristic
781C2×D4—28no—
782C2×D4—28no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—2924no—
822C22×C4—2924no—
823C22×C4—2924no—
824C22×C4—2924no—
825C22×C4—2924no—
826C22×C4—2924no—
827C22×C4—732no—
828C22×C4—732no—
829C22×C4—732no—
830C22×C4—732no—
831C22×C4—732no—
832C22×C4—732no—
833C22×C4—732no—
834C22×C4—732no—
835C22×C4—1461no—
836C22×C4—1461no—
837C22×C4—1461no—
838C22×C4—1461no—
839C22×C4—1461no—
840C22×C4—1461no—
841C22×C4—1461no—
842C22×C4—1461no—
843C22×C4—1461no—
844C22×C4—1461no—
845C22×C4—1461no—
846C22×C4—1461no—
847C22×C4—1461no—
848C22×C4—1461no—
849C22×C4—1468no—
850C22×C4—1461no—
851C22×C4—1461no—
852C22×C4—1461no—
853C22×C4—1461no—
854C22×C4—1461no—
855C22×C4—1461no—
856C22×C4—1461no—
857C22×C4—1461no—
858C22×C4—1461no—
859C22×C4—1461no—
860C22×C4—1461no—
861C22×C4—1461no—
862C22×C4—1461no—
863C22×C4—1461no—
864C22×C4—1461no—
865C22×C4—1461no—
866C22×C4—1461no—
867C22×C4—1461no—
868C22×C4—1461no—
869C22×C4—1461no—
870C22×C4—1461no—
871C22×C4—1461no—
872C22×C4—1461no—
873C22×C4—1461no—
874C22×C4—1461no—
875C22×C4—1461no—
876C22×C4—1461no—
877C22×C4—1461no—
878C22×C4—1461no—
879C22×C4—1461no—
880C22×C4—1461no—
881C22×C4—1461no—
882C22×C4—1461no—
883C22×C4—1461no—
884C22×C4C22×Dic7312yes—
885C22×C4C22×Dic7312yes—
886C22×C4C22×Dic7312yes—
887C22×C4C22×Dic7312yes—
888C22×C4C22×Dic7312yes—
889C22×C4D4×D7312yes—
890C22×C4D4×D7312yes—
891C22×C4#1192402712yes—
892C22×C4#1192402712yes—
893C4⋊C4—2924no—
894C4⋊C4—2924no—
895C4⋊C4—2924no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—2924no—
900C22⋊C4—2924no—
901C22⋊C4—2924no—
902C22⋊C4—2924no—
903C22⋊C4—1468no—
904C22⋊C4—1468no—
905C22⋊C4—1468no—
906C42—2924no—
907C42—2924no—
908C42—2924no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23#1455655014yes—
978C23D4×Dic7314yes—
979C23C23×Dic7311yescharacteristic
980C23C2×D4×D7311yescharacteristic
981C23C2×D4×D7311yescharacteristic
982C23C2×D4×D7311yescharacteristic
983C23#41×D7311yescharacteristic
984C23#41×D7311yescharacteristic
985C23C2×#1192402711yescharacteristic
986C23C2×#1192402711yescharacteristic
987C23C2×#1192402711yescharacteristic
988C23C2×#1192402811yescharacteristic
989C23C2×#1192402811yescharacteristic
990C23#1455663611yescharacteristic
991C23#1455663611yescharacteristic
992C23#1455663711yescharacteristic
993C23#1455663811yescharacteristic
994D4—416no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—416no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—2921no—
1030C2×C4—2921no—
1031C2×C4—2921no—
1032C2×C4—2921no—
1033C2×C4—2921no—
1034C2×C4—2921no—
1035C2×C4—2921no—
1036C2×C4—2921no—
1037C2×C4—2921no—
1038C2×C4—2921no—
1039C2×C4—2921no—
1040C2×C4—2921no—
1041C2×C4—2921no—
1042C2×C4—2921no—
1043C2×C4—2921no—
1044C2×C4—2921no—
1045C2×C4—2921no—
1046C2×C4—2921no—
1047C2×C4—2921no—
1048C2×C4—2921no—
1049C2×C4—29216no—
1050C2×C4—2921no—
1051C2×C4—2921no—
1052C2×C4—2921no—
1053C2×C4—2921no—
1054C2×C4—2921no—
1055C2×C4—2921no—
1056C2×C4—2921no—
1057C2×C4—2921no—
1058C2×C4—2921no—
1059C2×C4—2921no—
1060C2×C4—2921no—
1061C2×C4—2921no—
1062C2×C4—2921no—
1063C2×C4—2921no—
1064C2×C4—734no—
1065C2×C4—1462no—
1066C2×C4—1462no—
1067C2×C4—1462no—
1068C2×C4—1462no—
1069C2×C4—1462no—
1070C2×C4—1462no—
1071C2×C4—1462no—
1072C2×C4—1462no—
1073C2×C4—1462no—
1074C2×C4—1462no—
1075C2×C4—1462no—
1076C2×C4—1462no—
1077C2×C4—1462no—
1078C2×C4—1462no—
1079C2×C4—1462no—
1080C2×C4—1462no—
1081C2×C4—1462no—
1082C2×C4—1462no—
1083C2×C4—1462no—
1084C2×C4—1462no—
1085C2×C4—1462no—
1086C2×C4D4×Dic7314yes—
1087C2×C4D4×Dic7314yes—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22C2×#1455655011yescharacteristic
1119C22C2×D4×Dic7311yescharacteristic
1120C22C2×D4×Dic7311yescharacteristic
1121C22C2×D4×Dic7311yescharacteristic
1122C22#41×Dic7311yescharacteristic
1123C22#1798906211yescharacteristic
1124C22#1798907011yescharacteristic
1125C22#121×D7311yescharacteristic
1126C22#1798909611yescharacteristic
1127C22#1798909611yescharacteristic
1128C22#1798909711yescharacteristic
1129C22#1798911711yescharacteristic
1130C22#1798911711yescharacteristic
1131C22#1798911811yescharacteristic
1132C22#1798913211yescharacteristic
1133C22#1798917311yescharacteristic
1134C22#1798918011yescharacteristic
1135C22#1798918911yescharacteristic
1136C22#1798920511yescharacteristic
1137C22#1798921911yescharacteristic
1138C22#1798922111yescharacteristic
1139C22#1798922411yescharacteristic
1140C22#1798922411yescharacteristic
1141C22#1798922711yescharacteristic
1142C22#1798922711yescharacteristic
1143C22#1798923311yescharacteristic
1144C22#1798923711yescharacteristic
1145C22#1798924311yescharacteristic
1146C22#1798924611yescharacteristic
1147C22#1798926311yescharacteristic
1148C22#1798926311yescharacteristic
1149C22#1798926811yescharacteristic
1150C22#1798927711yescharacteristic
1151C22#1798928311yescharacteristic
1152C22#1798928911yescharacteristic
1153C4—24no—
1154C4—24no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—2922no—
1159C4—2922no—
1160C4—2922no—
1161C4—2922no—
1162C4—2922no—
1163C4—5841no—
1164C4—5841no—
1165C4—1464no—
1166C2—44no—
1167C2—44no—
1168C2#2261237611yescharacteristic
1169C2#121×Dic7311yescharacteristic
1170C2#2261272511yescharacteristic
1171C2#2261278011yescharacteristic
1172C2#2261286011yescharacteristic
1173C2#2261291511yescharacteristic
1174C2#2261295111yescharacteristic
1175C2#2261346611yescharacteristic
1176C2#2261350511yescharacteristic
1177C2#2261384311yescharacteristic
1178C2#2261392911yescharacteristic
1179C2#2261394111yescharacteristic
1180C2#2261413611yescharacteristic
1181C2#2261497311yescharacteristic
1182C2#2261526911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#386×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC2×#386D73
hypocenterC73#13988
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#17988480C2semidirect
3. C2×#17988462C2semidirect
4. C2×#17988447C2semidirect
5. C2×C22⋊C4×Dic73C2semidirect
6. C2×C4×C22⋊Dic73C2semidirect
7. #22608188C2semidirect
8. #22608180C2semidirect
9. #22608176C2semidirect
11. #22608168C2semidirect
12. #22608165C2semidirect
13. #22608165C2semidirect
14. #22608156C2semidirect
55. #386×C73C4semidirect
124. #14556498D4semidirect
125. #14556498D4semidirect
141. C23×C4×C73C2×C4semidirect
155. C2×C22⋊C4×C73C2×C4semidirect
156. #95×C73C2×C4semidirect
157. #95×C73C2×C4semidirect
607. C73#13988semidirect
629. #386Dic73semidirect
680. C23×C4C2×Dic73semidirect
724. C2×C22⋊C4C2×Dic73semidirect
748. #95C2×Dic73semidirect
749. #95C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884802
C2×#179884672
C2×#179884622
C2×#179884472
C2×C22⋊C4×Dic732
C2×C4×C22⋊Dic732
#226081882
#226081802
#226081762
#226081722
#226081682
#226081652
#226081562
C2×#386×C732
#1398873