Finite Group Databasebeta

← #33014157

Subgroups — #33014157

Order 18688.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988494C211yesmaximal, characteristic, complemented
2C2×#17988480C211yesmaximal, characteristic, complemented
3C2×#17988467C211yesmaximal, characteristic
4C2×#17988462C211yesmaximal, characteristic, complemented
5#22608202C211yesmaximal, characteristic, complemented
6#22608180C211yesmaximal, characteristic, complemented
7#22608176C211yesmaximal, characteristic, complemented
8#22608176C211yesmaximal, characteristic, complemented
9#22608176C211yesmaximal, characteristic, complemented
10#22608172C211yesmaximal, characteristic
11#22608168C211yesmaximal, characteristic, complemented
12#22608161C211yesmaximal, characteristic, complemented
13#22608158C211yesmaximal, characteristic, complemented
14#22608153C211yesmaximal, characteristic, complemented
15C22×#124×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
28#17988494—24no—
29#17988480—24no—
30#17988467—24no—
31#17988462—24no—
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C23×Q8×C73C2211yescharacteristic
49C23×D4×C73C2211yescharacteristic
50C2×#124×C73—24no—
51C2×#124×C73—24no—
52C2×#124×C73C418yescomplemented
53C22×C22⋊C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55C22×C22⋊C4×C73C2211yescharacteristic
56C22×C22⋊C4×C73C2211yescharacteristic
57C22×C42×C73C2211yescharacteristic
58C23×Dic73—22no—
59C23×Dic73—22no—
60C23×Dic73—22no—
61C23×Dic73—41no—
62C23×Dic73—41no—
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—41no—
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—41no—
92C2×C22⋊Dic73—41no—
93C2×C22⋊Dic73—41no—
94C2×C22⋊Dic73—41no—
95C2×C22⋊Dic73—41no—
96C2×C22⋊Dic73—41no—
97C2×C22⋊Dic73—41no—
98C2×C22⋊Dic73—41no—
99C2×C22⋊Dic73—41no—
100C2×C22⋊Dic73—41no—
101C2×C22⋊Dic73—41no—
102C2×C22⋊Dic73—41no—
103C2×C4×Dic73—22no—
104C2×C4×Dic73—22no—
105C2×C4×Dic73—41no—
106#14556498—22no—
107#14556498—22no—
108#14556498—22no—
109#14556498—22no—
110#14556498—22no—
111#14556498—22no—
112#14556498—22no—
113#14556498—22no—
114#14556498—22no—
115#14556498—41no—
116#14556498—41no—
117#14556498—41no—
118#14556498—41no—
119#14556498—41no—
120#14556498—41no—
121#14556498D414yes—
122C25×C73C2311yescharacteristic
123C25×C73C2311yescharacteristic
124C22×Q8×C73—22no—
125C22×Q8×C73—22no—
126C22×Q8×C73—22no—
127C22×Q8×C73—22no—
128C22×Q8×C73—41no—
129C22×Q8×C73—41no—
130C22×Q8×C73C2×C414yescomplemented
131C22×D4×C73—22no—
132C22×D4×C73—22no—
133C22×D4×C73—22no—
134C22×D4×C73—22no—
135C22×D4×C73—41no—
136C22×D4×C73—41no—
137C22×D4×C73C2×C414yes—
138C23×C4×C73C2311yescharacteristic
139C23×C4×C73C2311yescharacteristic
140C23×C4×C73C2311yescharacteristic
141C23×C4×C73C2311yescharacteristic
142C23×C4×C73C2311yescharacteristic
143#124×C73—232no—
144C2×C22⋊C4×C73—22no—
145C2×C22⋊C4×C73—22no—
146C2×C22⋊C4×C73—22no—
147C2×C22⋊C4×C73—22no—
148C2×C22⋊C4×C73—22no—
149C2×C22⋊C4×C73—22no—
150C2×C22⋊C4×C73C2×C414yes—
151C2×C22⋊C4×C73C2×C414yes—
152C2×C22⋊C4×C73C2×C414yescomplemented
153C2×C22⋊C4×C73C2×C414yescomplemented
154C2×C22⋊C4×C73D414yes—
155C2×C22⋊C4×C73D414yes—
156C2×C42×C73—22no—
157C2×C42×C73—22no—
158C2×C42×C73C2×C414yescomplemented
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×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—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—44no—
212C22×Dic73—44no—
213C22×Dic73—44no—
214C22×Dic73—44no—
215C22×Dic73—44no—
216C22×Dic73—44no—
217C22×Dic73—44no—
218C22×Dic73C2×D412yes—
219C22×Dic73C2×D412yes—
220C22×Dic73#4112yes—
221C22×Dic73#4112yes—
222C4⋊Dic73—44no—
223C4⋊Dic73—44no—
224C4⋊Dic73—44no—
225C22⋊Dic73—44no—
226C22⋊Dic73—44no—
227C22⋊Dic73—44no—
228C22⋊Dic73—44no—
229C22⋊Dic73—44no—
230C22⋊Dic73—44no—
231C22⋊Dic73—44no—
232C4×Dic73—44no—
233C24×C73—21no—
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×C73—21no—
259C24×C73C22×C412yes—
260C24×C73C22×C412yes—
261C24×C73C2×D412yes—
262C24×C73C2×D412yes—
263C24×C73C2411yescharacteristic
264C2×Q8×C73—28no—
265C2×Q8×C73—28no—
266C2×Q8×C73—44no—
267C2×Q8×C73—44no—
268C2×Q8×C73—44no—
269C2×Q8×C73—44no—
270C2×Q8×C73—44no—
271C2×D4×C73—28no—
272C2×D4×C73—28no—
273C2×D4×C73—44no—
274C2×D4×C73—44no—
275C2×D4×C73—44no—
276C2×D4×C73—44no—
277C2×D4×C73—44no—
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—21no—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73C22×C412yes—
303C22×C4×C73C22×C412yes—
304C22×C4×C73C22×C412yes—
305C22×C4×C73C22×C412yes—
306C22×C4×C73C22×C412yes—
307C22×C4×C73C2×D412yes—
308C22×C4×C73C2×D412yes—
309C22×C4×C73C2×D412yes—
310C22×C4×C73C2×D412yes—
311C22×C4×C73C2×D412yes—
312C22×C4×C73#4112yes—
313C22⋊C4×C73—28no—
314C22⋊C4×C73—28no—
315C22⋊C4×C73—28no—
316C22⋊C4×C73C22⋊C4116yescomplemented
317C42×C73—28no—
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—41no—
344C23×C73—41no—
345C23×C73—41no—
346C23×C73—41no—
347C23×C73—41no—
348C23×C73—41no—
349C23×C73—41no—
350C23×C73—41no—
351C23×C73—41no—
352C23×C73—41no—
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—41no—
386C23×C73—41no—
387C23×C73C2×C22⋊C414yes—
388C23×C73C23×C411yescharacteristic
389C23×C73C22×D411yescharacteristic
390C23×C73C22×D411yescharacteristic
391C23×C73C22×D411yescharacteristic
392C23×C73C2×#4111yescharacteristic
393C23×C73C2×#4111yescharacteristic
394C23×C73C2×#4111yescharacteristic
395C23×C73H(5,𝔽2)11yescharacteristic
396C23×C73H(5,𝔽2)11yescharacteristic
397C23×C73H(5,𝔽2)11yescharacteristic
398C23×C73H(5,𝔽2)11yescharacteristic
399C23×C73H(5,𝔽2)11yescharacteristic
400C23×C732−1+411yescharacteristic
401C23×C732−1+411yescharacteristic
402C23×C732−1+411yescharacteristic
403Q8×C73—416no—
404D4×C73—416no—
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—22no—
425C2×C4×C73—22no—
426C2×C4×C73—22no—
427C2×C4×C73—22no—
428C2×C4×C73—22no—
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×C73C2×C22⋊C414yes—
438C2×C4×C73C2×C22⋊C414yes—
439C2×C4×C73C4×D414yes—
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—416no—
453C2×Dic73—41no—
454C2×Dic73—41no—
455C2×Dic73—41no—
456C2×Dic73—41no—
457C2×Dic73—41no—
458C2×Dic73—41no—
459C2×Dic73—41no—
460C2×Dic73—41no—
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—41no—
496C2×Dic73—41no—
497C22×C73—24no—
498C22×C73—24no—
499C22×C73—24no—
500C22×C73—42no—
501C22×C73—42no—
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—81no—
520C22×C73—81no—
521C22×C73—81no—
522C22×C73—81no—
523C22×C73—81no—
524C22×C73—81no—
525C22×C73—81no—
526C22×C73—81no—
527C22×C73C22×C22⋊C411yescharacteristic
528C22×C73C2×C4×D411yescharacteristic
529C22×C73C4×#4111yescharacteristic
530C22×C73#51811yescharacteristic
531C22×C73#52011yescharacteristic
532C22×C73#52011yescharacteristic
533C22×C73#52011yescharacteristic
534C22×C73#53511yescharacteristic
535C22×C73#53511yescharacteristic
536C22×C73#53611yescharacteristic
537C22×C73#53611yescharacteristic
538C22×C73#53711yescharacteristic
539C22×C73#53711yescharacteristic
540C22×C73#53811yescharacteristic
541C22×C73#53811yescharacteristic
542C22×C73#54211yescharacteristic
543C22×C73#54211yescharacteristic
544C22×C73#54211yescharacteristic
545C22×C73#54211yescharacteristic
546C22×C73D4211yescharacteristic
547C22×C73D4211yescharacteristic
548C22×C73#54611yescharacteristic
549C22×C73#54611yescharacteristic
550C22×C73#54611yescharacteristic
551C22×C73#54611yescharacteristic
552C22×C73#54611yescharacteristic
553C22×C73#54711yescharacteristic
554C22×C73#54711yescharacteristic
555C22×C73#54811yescharacteristic
556C22×C73#55611yescharacteristic
557C22×C73#55911yescharacteristic
558C22×C73H(3,𝔽4)11yescharacteristic
559C22×C73#56211yescharacteristic
560C22×C73#56211yescharacteristic
561C22×C73#56311yescharacteristic
562C4×C73—24no—
563C4×C73—24no—
564C4×C73—24no—
565C4×C73—42no—
566C4×C73—42no—
567Dic73—42no—
568Dic73—42no—
569Dic73—42no—
570Dic73—42no—
571Dic73—81no—
572Dic73—81no—
573Dic73—81no—
574Dic73—81no—
575#14421—731nomaximal, Sylow
576C2×C73—44no—
577C2×C73—82no—
578C2×C73#231111yescharacteristic
579C2×C73#232611yescharacteristic
580C2×C73#233711yescharacteristic
581C2×C73D4×C22⋊C411yescharacteristic
582C2×C73#233911yescharacteristic
583C2×C73#236711yescharacteristic
584C2×C73#237911yescharacteristic
585C2×C73#267011yescharacteristic
586C2×C73#267211yescharacteristic
587C2×C73#267411yescharacteristic
588C2×C73#267611yescharacteristic
589C2×C73#270011yescharacteristic
590C2×C73#271011yescharacteristic
591C2×C73#271211yescharacteristic
592C2×C73#271511yescharacteristic
593C22×#124D7311yescharacteristic
594C2×#391—731no—
595C2×#388—731no—
596C2×#386—731no—
597C2×#385—731no—
598#1446—731no—
599#1440—731no—
600#1439—731no—
601#1439—731no—
602#1439—731no—
603#1438—731no—
604#1437—731no—
605C4⋊#95—731no—
606#1434—731no—
607C22⋊#95—731no—
608C73#1442111yescharacteristic, complemented, Sylow
609C23×Q8C2×D7311yescharacteristic
610C23×D4C2×D7311yescharacteristic
611C24×C4—731no—
612C2×#124—24no—
613C2×#124—24no—
614C2×#124Dic7318yescomplemented
615C22×C4⋊C4—731no—
616C22×C4⋊C4—731no—
617C22×C4⋊C4—731no—
618C22×C22⋊C4—731no—
619C22×C22⋊C4—731no—
620C22×C22⋊C4—731no—
621C22×C22⋊C4—731no—
622C22×C22⋊C4—731no—
623C22×C22⋊C4—731no—
624C22×C22⋊C4—731no—
625C22×C22⋊C4C2×D7311yescharacteristic
626C22×C22⋊C4C2×D7311yescharacteristic
627C22×C22⋊C4C2×D7311yescharacteristic
628C22×C22⋊C4C2×D7311yescharacteristic
629C22×C42—731no—
630C22×C42C2×D7311yescharacteristic
631#391—1464no—
632#388—1464no—
633#386—1464no—
634#385—1464no—
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×#95—731no—
649C2×#95—731no—
650C2×#95—731no—
651C25C22×D7311yescharacteristic
652C25C22×D7311yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×Dic7314yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×Dic7314yes—
667C23×C4—2921no—
668C23×C4—2921no—
669C23×C4—2921no—
670C23×C4—2921no—
671C23×C4—731no—
672C23×C4—731no—
673C23×C4—731no—
674C23×C4—731no—
675C23×C4—731no—
676C23×C4—731no—
677C23×C4—731no—
678C23×C4—731no—
679C23×C4—1462no—
680C23×C4—1462no—
681C23×C4—1462no—
682C23×C4C22×D7311yescharacteristic
683C23×C4C22×D7311yescharacteristic
684C23×C4C22×D7311yescharacteristic
685C23×C4C22×D7311yescharacteristic
686C23×C4C22×D7311yescharacteristic
687#124—232no—
688C2×C4⋊C4—2921no—
689C2×C4⋊C4—2921no—
690C2×C4⋊C4—2921no—
691C2×C4⋊C4—1462no—
692C2×C4⋊C4—1462no—
693C2×C4⋊C4—1462no—
694C2×C4⋊C4—1462no—
695C2×C4⋊C4—1462no—
696C2×C4⋊C4—1462no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—2921no—
704C2×C22⋊C4—2921no—
705C2×C22⋊C4—2921no—
706C2×C22⋊C4—2921no—
707C2×C22⋊C4—2921no—
708C2×C22⋊C4—2921no—
709C2×C22⋊C4—2921no—
710C2×C22⋊C4—2921no—
711C2×C22⋊C4—2921no—
712C2×C22⋊C4—2921no—
713C2×C22⋊C4—2921no—
714C2×C22⋊C4—2921no—
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⋊C4—1462no—
723C2×C22⋊C4—1462no—
724C2×C22⋊C4C2×Dic7314yes—
725C2×C22⋊C4C2×Dic7314yes—
726C2×C22⋊C4C2×Dic7314yescomplemented
727C2×C22⋊C4C2×Dic7314yescomplemented
728C2×C22⋊C4C22⋊D7314yes—
729C2×C22⋊C4C22⋊D7314yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—2921no—
733C2×C42—1462no—
734C2×C42—1462no—
735C2×C42C2×Dic7314yescomplemented
736#95—2921no—
737#95—2921no—
738#95—2921no—
739#95—2921no—
740#95—2921no—
741#95—2921no—
742#95—734no—
743#95—1462no—
744#95—1462no—
745#95—1462no—
746#95—1462no—
747#95—1462no—
748#95—1462no—
749#95—1462no—
750#95—1462no—
751#95—1462no—
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—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×Dic7312yes—
779C24C22×Dic7312yes—
780C24C2×C22⋊D7312yes—
781C24C2×C22⋊D7312yes—
782C24C23×D7311yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
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—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—2924no—
822C22×C4—2924no—
823C22×C4—2924no—
824C22×C4—2924no—
825C22×C4—2924no—
826C22×C4—2924no—
827C22×C4—2924no—
828C22×C4—732no—
829C22×C4—732no—
830C22×C4—732no—
831C22×C4—732no—
832C22×C4—1461no—
833C22×C4—1461no—
834C22×C4—1461no—
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—1461no—
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×C4C2×C22⋊D7312yes—
891C22×C4C2×C22⋊D7312yes—
892C22×C4C2×C22⋊D7312yes—
893C22×C4C2×C22⋊D7312yes—
894C22×C4#1192402712yes—
895C4⋊C4—2924no—
896C4⋊C4—2924no—
897C4⋊C4—2924no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—2924no—
902C22⋊C4—2924no—
903C22⋊C4—2924no—
904C22⋊C4—2924no—
905C22⋊C4—2924no—
906C22⋊C4—2924no—
907C22⋊C4—2924no—
908C22⋊C4C22⋊Dic73116yescomplemented
909C42—28no—
910C42—2924no—
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—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
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—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊Dic7314yes—
981C23C23×Dic7311yescharacteristic
982C23C2×D4×D7311yescharacteristic
983C23C22×C22⋊D7311yescharacteristic
984C23C22×C22⋊D7311yescharacteristic
985C23#41×D7311yescharacteristic
986C23#41×D7311yescharacteristic
987C23C2×#1192402711yescharacteristic
988C23#1455663611yescharacteristic
989C23#1455663611yescharacteristic
990C23#1455663711yescharacteristic
991C23#1455663711yescharacteristic
992C23#1455663711yescharacteristic
993C23#1455663811yescharacteristic
994C23#1455663811yescharacteristic
995C23#1455663811yescharacteristic
996Q8—416no—
997D4—416no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—29216no—
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—2921no—
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—2921no—
1065C2×C4—2921no—
1066C2×C4—2921no—
1067C2×C4—2921no—
1068C2×C4—2921no—
1069C2×C4—2921no—
1070C2×C4—2921no—
1071C2×C4—2921no—
1072C2×C4—2921no—
1073C2×C4—2921no—
1074C2×C4—2921no—
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×C4—1462no—
1087C2×C4C2×C22⋊Dic7314yes—
1088C2×C4C2×C22⋊Dic7314yes—
1089C2×C4D4×Dic7314yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
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—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊Dic7311yescharacteristic
1121C22C2×D4×Dic7311yescharacteristic
1122C22#41×Dic7311yescharacteristic
1123C22#1798906211yescharacteristic
1124C22#1798907011yescharacteristic
1125C22#1798907011yescharacteristic
1126C22#1798907011yescharacteristic
1127C22#1798915111yescharacteristic
1128C22#1798915511yescharacteristic
1129C22#1798915711yescharacteristic
1130C22#1798915811yescharacteristic
1131C22#1798916511yescharacteristic
1132C22#1798916511yescharacteristic
1133C22#1798917111yescharacteristic
1134C22#1798917111yescharacteristic
1135C22#1798920111yescharacteristic
1136C22#1798920111yescharacteristic
1137C22#1798920611yescharacteristic
1138C22#1798920611yescharacteristic
1139C22D4×C22⋊D7311yescharacteristic
1140C22D4×C22⋊D7311yescharacteristic
1141C22#1798922511yescharacteristic
1142C22#1798922511yescharacteristic
1143C22#1798923011yescharacteristic
1144C22#1798923111yescharacteristic
1145C22#1798923111yescharacteristic
1146C22#1798923611yescharacteristic
1147C22#1798923611yescharacteristic
1148C22#1798924511yescharacteristic
1149C22#1798930611yescharacteristic
1150C22#1798931911yescharacteristic
1151C22#1798932911yescharacteristic
1152C22#1798933111yescharacteristic
1153C22#1798933111yescharacteristic
1154C22#1798933711yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—2922no—
1161C4—2922no—
1162C4—2922no—
1163C4—2922no—
1164C4—5841no—
1165C4—5841no—
1166C4—5841no—
1167C4—5841no—
1168C2—44no—
1169C2—82no—
1170C2#2261252311yescharacteristic
1171C2#2261264411yescharacteristic
1172C2#2261274611yescharacteristic
1173C2D4×C22⋊Dic7311yescharacteristic
1174C2#2261276111yescharacteristic
1175C2#2261300611yescharacteristic
1176C2#2261310511yescharacteristic
1177C2#2261615211yescharacteristic
1178C2#2261617711yescharacteristic
1179C2#2261620611yescharacteristic
1180C2#2261622711yescharacteristic
1181C2#2261652311yescharacteristic
1182C2#2261666711yescharacteristic
1183C2#2261669711yescharacteristic
1184C2#2261673611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC22×#124×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC22×#124D73
hypocenterC73#14421
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#17988494C2semidirect
2. C2×#17988480C2semidirect
4. C2×#17988462C2semidirect
5. #22608202C2semidirect
6. #22608180C2semidirect
7. #22608176C2semidirect
8. #22608176C2semidirect
9. #22608176C2semidirect
11. #22608168C2semidirect
12. #22608161C2semidirect
13. #22608158C2semidirect
14. #22608153C2semidirect
52. C2×#124×C73C4semidirect
130. C22×Q8×C73C2×C4semidirect
152. C2×C22⋊C4×C73C2×C4semidirect
153. C2×C22⋊C4×C73C2×C4semidirect
158. C2×C42×C73C2×C4semidirect
316. C22⋊C4×C73C22⋊C4semidirect
608. C73#14421semidirect
614. C2×#124Dic73semidirect
659. C22×Q8C2×Dic73semidirect
726. C2×C22⋊C4C2×Dic73semidirect
727. C2×C22⋊C4C2×Dic73semidirect
735. C2×C42C2×Dic73semidirect
908. C22⋊C4C22⋊Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884942
C2×#179884802
C2×#179884672
C2×#179884622
#226082022
#226081802
#226081762
#226081722
#226081682
#226081612
#226081582
#226081532
C22×#124×C732
#1442173