Finite Group Databasebeta

← #33007482

Subgroups — #33007482

Order 18688.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556551C211yesmaximal, characteristic
2C2×#17988466C211yesmaximal, characteristic
3C2×#17988464C211yesmaximal, characteristic
4C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
5C2×C4×#11924005C211yesmaximal, characteristic, complemented
6C22×#14556498C211yesmaximal, characteristic, complemented
7#22608169C211yesmaximal, characteristic, complemented
8#22608167C211yesmaximal, characteristic, complemented
9#22608166C211yesmaximal, characteristic, complemented
10#22608164C211yesmaximal, characteristic, complemented
11#22608155C211yesmaximal, characteristic, complemented
12#22608153C211yesmaximal, characteristic, complemented
13#22608152C211yesmaximal, characteristic, complemented
14C4×#14556498C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C23×C22⋊D73C2211yescharacteristic
17C24×Dic73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C2×#14556551—24no—
21C2×#14556551—24no—
22C2×#14556551C418yescomplemented
23C22×#11924007C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×#11924005C2211yescharacteristic
26C22×#11924005C2211yescharacteristic
27C22×#11924005C2211yescharacteristic
28C22×#11924005C2211yescharacteristic
29C22×#11924005C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33#17988466C418yescomplemented
34#17988464C418yescomplemented
35C22⋊C4×Dic73—24no—
36C4×#11924005—24no—
37C2×#14556498—24no—
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C24×C4×C73C2211yescharacteristic
53C22×C22⋊C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55C22×C42×C73C2211yescharacteristic
56C22×C42×C73C2211yescharacteristic
57C4×C22⋊C4×C73—24no—
58C2×#95×C73C2211yescharacteristic
59C2×#95×C73C2211yescharacteristic
60C24×D73C2311yescharacteristic
61C22×C22⋊D73—22no—
62C22×C22⋊D73—22no—
63C22×C22⋊D73—22no—
64C22×C22⋊D73—22no—
65C22×C22⋊D73C2×C414yes—
66C22×C22⋊D73C2×C414yes—
67C22×C22⋊D73C2×C414yes—
68C23×Dic73—22no—
69C23×Dic73—22no—
70C23×Dic73—22no—
71C23×Dic73—22no—
72C23×Dic73—22no—
73C23×Dic73—22no—
74C23×Dic73—22no—
75C23×Dic73—22no—
76C23×Dic73—41no—
77C23×Dic73—41no—
78C23×Dic73—41no—
79C23×Dic73—41no—
80C23×Dic73C2×C414yes—
81C23×Dic73C2×C414yescomplemented
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2311yescharacteristic
84C23×Dic73C2311yescharacteristic
85C23×Dic73C2311yescharacteristic
86C23×Dic73C2311yescharacteristic
87C23×Dic73C2311yescharacteristic
88C23×Dic73C2311yescharacteristic
89C22×C4×D73—22no—
90C22×C4×D73—22no—
91C22×C4×D73—22no—
92C22×C4×D73—22no—
93C22×C4×D73—41no—
94C22×C4×D73—41no—
95C22×C4×D73C2×C414yescomplemented
96#14556551—232no—
97C2×#11924007—22no—
98C2×#11924007—22no—
99C2×#11924007C2×C414yescomplemented
100C2×C22⋊Dic73—22no—
101C2×C22⋊Dic73—22no—
102C2×C22⋊Dic73C2×C414yescomplemented
103C2×#11924005—22no—
104C2×#11924005—22no—
105C2×#11924005—22no—
106C2×#11924005—22no—
107C2×#11924005—22no—
108C2×#11924005—22no—
109C2×#11924005—41no—
110C2×#11924005—41no—
111C2×#11924005—41no—
112C2×#11924005—41no—
113C2×#11924005C2×C414yescomplemented
114C2×#11924005C2×C414yescomplemented
115C2×#11924005C2×C414yescomplemented
116C2×#11924005C2×C414yescomplemented
117C2×#11924005C2×C414yescomplemented
118C2×C4×Dic73—22no—
119C2×C4×Dic73—22no—
120C2×C4×Dic73—22no—
121C2×C4×Dic73—22no—
122C2×C4×Dic73—22no—
123C2×C4×Dic73—22no—
124C2×C4×Dic73—41no—
125C2×C4×Dic73—41no—
126C2×C4×Dic73C2×C414yescomplemented
127#14556498—22no—
128#14556498—22no—
129#14556498—22no—
130#14556498—22no—
131#14556498—22no—
132#14556498—22no—
133#14556498—22no—
134#14556498—41no—
135#14556498—41no—
136#14556498C2×C414yescomplemented
137#14556498C2×C414yescomplemented
138#14556498C2×C414yescomplemented
139#14556498C2×C414yescomplemented
140#14556498D414yescomplemented
141C25×C73C2311yescharacteristic
142C23×C4×C73—22no—
143C23×C4×C73—22no—
144C23×C4×C73—22no—
145C23×C4×C73—22no—
146C23×C4×C73—41no—
147C23×C4×C73—41no—
148C23×C4×C73C2×C414yescomplemented
149C23×C4×C73C2311yescharacteristic
150C23×C4×C73C2311yescharacteristic
151C23×C4×C73C2311yescharacteristic
152C23×C4×C73C2311yescharacteristic
153C23×C4×C73C2311yescharacteristic
154C23×C4×C73C2311yescharacteristic
155C2×C22⋊C4×C73—22no—
156C2×C22⋊C4×C73—22no—
157C2×C22⋊C4×C73C2×C414yes—
158C2×C22⋊C4×C73C2×C414yescomplemented
159C2×C22⋊C4×C73D414yes—
160C2×C22⋊C4×C73D414yes—
161C2×C42×C73—22no—
162C2×C42×C73—22no—
163C2×C42×C73—22no—
164C2×C42×C73—22no—
165C2×C42×C73—41no—
166C2×C42×C73—41no—
167#95×C73—22no—
168#95×C73—22no—
169C23×D73—21no—
170C23×D73—21no—
171C23×D73—21no—
172C23×D73—21no—
173C23×D73—21no—
174C23×D73—21no—
175C23×D73—21no—
176C23×D73—21no—
177C23×D73—21no—
178C23×D73—21no—
179C23×D73—21no—
180C23×D73—21no—
181C23×D73C22×C412yes—
182C23×D73C22×C412yes—
183C23×D73C22×C412yes—
184C2×C22⋊D73—28no—
185C2×C22⋊D73—28no—
186C2×C22⋊D73—28no—
187C2×C22⋊D73—28no—
188C2×C22⋊D73—28no—
189C2×C22⋊D73—28no—
190C2×C22⋊D73C42116yescomplemented
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—28no—
204C22×Dic73—28no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73—21no—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C22×Dic73—21no—
220C22×Dic73—21no—
221C22×Dic73—21no—
222C22×Dic73—21no—
223C22×Dic73—21no—
224C22×Dic73—21no—
225C22×Dic73—21no—
226C22×Dic73—21no—
227C22×Dic73—21no—
228C22×Dic73—21no—
229C22×Dic73—28no—
230C22×Dic73—28no—
231C22×Dic73—44no—
232C22×Dic73—44no—
233C22×Dic73—44no—
234C22×Dic73—44no—
235C22×Dic73—44no—
236C22×Dic73—44no—
237C22×Dic73—44no—
238C22×Dic73—44no—
239C22×Dic73—44no—
240C22×Dic73—44no—
241C22×Dic73C22×C412yes—
242C22×Dic73C22×C412yes—
243C22×Dic73C22×C412yes—
244C22×Dic73C22×C412yes—
245C22×Dic73C22×C412yes—
246C22×Dic73C22×C412yes—
247C22×Dic73C22×C412yes—
248C22×Dic73C22×C412yes—
249C22×Dic73C22×C412yes—
250C22×Dic73C2×D412yes—
251C22×Dic73C2×D412yes—
252C22×Dic73#4112yes—
253C22×Dic73#4112yes—
254C2×C4×D73—28no—
255C2×C4×D73—28no—
256C2×C4×D73—44no—
257C2×C4×D73—44no—
258C2×C4×D73—44no—
259C2×C4×D73—44no—
260C2×C4×D73—44no—
261#11924007—28no—
262C22⋊Dic73—28no—
263#11924005—28no—
264#11924005—28no—
265#11924005—28no—
266#11924005—44no—
267#11924005—44no—
268C4×Dic73—28no—
269C4×Dic73—44no—
270C4×Dic73—44no—
271C24×C73—21no—
272C24×C73—21no—
273C24×C73—21no—
274C24×C73—21no—
275C24×C73—21no—
276C24×C73—21no—
277C24×C73—21no—
278C24×C73—21no—
279C24×C73C22×C412yes—
280C24×C73C22×C412yes—
281C24×C73C22×C412yes—
282C24×C73C2×D412yes—
283C24×C73C2×D412yes—
284C24×C73#4112yes—
285C24×C73#4112yes—
286C24×C73C2411yescharacteristic
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—28no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73—21no—
303C22×C4×C73—21no—
304C22×C4×C73—21no—
305C22×C4×C73—21no—
306C22×C4×C73—21no—
307C22×C4×C73—21no—
308C22×C4×C73—21no—
309C22×C4×C73—21no—
310C22×C4×C73—21no—
311C22×C4×C73—21no—
312C22×C4×C73—21no—
313C22×C4×C73—21no—
314C22×C4×C73—21no—
315C22×C4×C73—21no—
316C22×C4×C73—21no—
317C22×C4×C73—21no—
318C22×C4×C73—28no—
319C22×C4×C73—44no—
320C22×C4×C73—44no—
321C22×C4×C73—44no—
322C22×C4×C73—44no—
323C22×C4×C73—44no—
324C22×C4×C73C22×C412yes—
325C22×C4×C73C22×C412yes—
326C22×C4×C73C22×C412yes—
327C22×C4×C73C22×C412yes—
328C22×C4×C73C22×C412yes—
329C22×C4×C73C22×C412yes—
330C22×C4×C73C2×D412yes—
331C22×C4×C73C2×D412yes—
332C22×C4×C73C2×D412yes—
333C22×C4×C73C2×D412yes—
334C22×C4×C73C2×D412yes—
335C22×C4×C73#4112yes—
336C22⋊C4×C73—28no—
337C22⋊C4×C73C22⋊C4116yescomplemented
338C42×C73—44no—
339C42×C73—44no—
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—22no—
354C23×C73—22no—
355C23×C73—22no—
356C23×C73—22no—
357C23×C73—22no—
358C23×C73—22no—
359C23×C73—22no—
360C23×C73—22no—
361C23×C73—22no—
362C23×C73—22no—
363C23×C73—22no—
364C23×C73—22no—
365C23×C73—22no—
366C23×C73—22no—
367C23×C73—22no—
368C23×C73C2×C4214yes—
369C23×C73C2×C22⋊C414yes—
370C23×C73#11714yes—
371C23×C73C4×D414yes—
372C23×C73C4×D414yes—
373C23×C73C4×D414yes—
374C23×C73C4×D414yes—
375C23×C73C23×C411yescharacteristic
376C23×C73C23×C411yescharacteristic
377C23×C73C23×C411yescharacteristic
378C23×C73C22×D411yescharacteristic
379C23×C73C22×D411yescharacteristic
380C23×C73C22×D411yescharacteristic
381C23×C73C2×#4111yescharacteristic
382C23×C73C2×#4111yescharacteristic
383C23×C73C2×#4111yescharacteristic
384C23×C73C2×#4111yescharacteristic
385C23×C73C2×#4111yescharacteristic
386C23×C73H(5,𝔽2)11yescharacteristic
387C23×C73H(5,𝔽2)11yescharacteristic
388C23×C73H(5,𝔽2)11yescharacteristic
389C23×C732−1+411yescharacteristic
390C22×D73—22no—
391C22×D73—22no—
392C22×D73—22no—
393C22×D73—22no—
394C22×D73—22no—
395C22×D73—22no—
396C22×D73—22no—
397C22×D73—22no—
398C22×D73—22no—
399C22×D73—22no—
400C22×D73—22no—
401C22×D73—22no—
402C22×D73—22no—
403C22×D73—22no—
404C22×D73—22no—
405C22×D73—22no—
406C22×D73—22no—
407C22×D73—22no—
408C22×D73—41no—
409C22×D73—41no—
410C22×D73—41no—
411C22×D73—41no—
412C22×D73—41no—
413C22×D73—41no—
414C22×D73—41no—
415C22×D73—41no—
416C22×D73—41no—
417C22×D73—41no—
418C22×D73—41no—
419C22×D73—41no—
420C22×D73—41no—
421C22×D73—41no—
422C22×D73—41no—
423C22×D73—41no—
424C22×D73C2×C4214yes—
425C2×C4×C73—22no—
426C2×C4×C73—22no—
427C2×C4×C73—22no—
428C2×C4×C73—22no—
429C2×C4×C73—22no—
430C2×C4×C73—22no—
431C2×C4×C73—22no—
432C2×C4×C73—22no—
433C2×C4×C73—22no—
434C2×C4×C73—22no—
435C2×C4×C73—22no—
436C2×C4×C73—22no—
437C2×C4×C73—22no—
438C2×C4×C73—22no—
439C2×C4×C73—22no—
440C2×C4×C73—22no—
441C2×C4×C73—22no—
442C2×C4×C73—22no—
443C2×C4×C73—22no—
444C2×C4×C73—22no—
445C2×C4×C73—22no—
446C2×C4×C73—22no—
447C2×C4×C73—22no—
448C2×C4×C73—22no—
449C2×C4×C73—22no—
450C2×C4×C73—22no—
451C2×C4×C73—22no—
452C2×C4×C73—416no—
453C2×C4×C73—41no—
454C2×C4×C73—41no—
455C2×C4×C73—41no—
456C2×C4×C73—41no—
457C2×C4×C73—41no—
458C2×C4×C73—41no—
459C2×C4×C73—41no—
460C2×C4×C73—41no—
461C2×C4×C73—41no—
462C2×C4×C73—41no—
463C2×C4×C73—41no—
464C2×C4×C73—41no—
465C2×C4×C73C2×C22⋊C414yes—
466C2×C4×C73C2×C22⋊C414yes—
467C2×C4×C73C4×D414yescomplemented
468C22⋊D73—232no—
469C2×Dic73—22no—
470C2×Dic73—22no—
471C2×Dic73—22no—
472C2×Dic73—22no—
473C2×Dic73—22no—
474C2×Dic73—22no—
475C2×Dic73—22no—
476C2×Dic73—22no—
477C2×Dic73—22no—
478C2×Dic73—22no—
479C2×Dic73—22no—
480C2×Dic73—22no—
481C2×Dic73—22no—
482C2×Dic73—22no—
483C2×Dic73—22no—
484C2×Dic73—22no—
485C2×Dic73—22no—
486C2×Dic73—22no—
487C2×Dic73—22no—
488C2×Dic73—22no—
489C2×Dic73—22no—
490C2×Dic73—22no—
491C2×Dic73—22no—
492C2×Dic73—22no—
493C2×Dic73—22no—
494C2×Dic73—22no—
495C2×Dic73—22no—
496C2×Dic73—22no—
497C2×Dic73—22no—
498C2×Dic73—22no—
499C2×Dic73—416no—
500C2×Dic73—416no—
501C2×Dic73—41no—
502C2×Dic73—41no—
503C2×Dic73—41no—
504C2×Dic73—41no—
505C2×Dic73—41no—
506C2×Dic73—41no—
507C2×Dic73—41no—
508C2×Dic73—41no—
509C2×Dic73—41no—
510C2×Dic73—41no—
511C2×Dic73—41no—
512C2×Dic73—41no—
513C2×Dic73—41no—
514C2×Dic73—41no—
515C2×Dic73—41no—
516C2×Dic73—41no—
517C2×Dic73C2×C4214yes—
518C2×Dic73C4×D414yes—
519C2×Dic73C4×D414yescomplemented
520C4×D73—416no—
521C22×C73—24no—
522C22×C73—24no—
523C22×C73—24no—
524C22×C73—24no—
525C22×C73—24no—
526C22×C73—24no—
527C22×C73—24no—
528C22×C73—24no—
529C22×C73—24no—
530C22×C73—24no—
531C22×C73—24no—
532C22×C73—24no—
533C22×C73—24no—
534C22×C73—24no—
535C22×C73C4×C22⋊C418yescomplemented
536C22×C73C22×C4211yescharacteristic
537C22×C73C22×C22⋊C411yescharacteristic
538C22×C73C2×#11711yescharacteristic
539C22×C73C2×C4×D411yescharacteristic
540C22×C73C2×C4×D411yescharacteristic
541C22×C73C2×C4×D411yescharacteristic
542C22×C73C2×C4×D411yescharacteristic
543C22×C73C2×C4×D411yescharacteristic
544C22×C73C2×C4×D411yescharacteristic
545C22×C73C2×C4×D411yescharacteristic
546C22×C73C4×#4111yescharacteristic
547C22×C73C4×#4111yescharacteristic
548C22×C73C4×#4111yescharacteristic
549C22×C73#51811yescharacteristic
550C22×C73#51811yescharacteristic
551C22×C73#51811yescharacteristic
552C22×C73#52011yescharacteristic
553C22×C73#52011yescharacteristic
554C22×C73#52011yescharacteristic
555C22×C73D4211yescharacteristic
556C22×C73D4211yescharacteristic
557C22×C73#54611yescharacteristic
558C22×C73#54611yescharacteristic
559C22×C73#54611yescharacteristic
560C22×C73#54611yescharacteristic
561C22×C73#54611yescharacteristic
562C22×C73#54711yescharacteristic
563C22×C73#54711yescharacteristic
564C22×C73#54811yescharacteristic
565C22×C73#55111yescharacteristic
566C22×C73#55111yescharacteristic
567C22×C73#55211yescharacteristic
568C22×C73#55311yescharacteristic
569C22×C73#55311yescharacteristic
570C22×C73#55311yescharacteristic
571C2×D73—24no—
572C2×D73—24no—
573C2×D73—24no—
574C2×D73—42no—
575C2×D73—42no—
576C2×D73—42no—
577C2×D73—42no—
578C2×D73—42no—
579C2×D73—42no—
580C2×D73—42no—
581C2×D73—42no—
582C2×D73—42no—
583C2×D73—42no—
584C2×D73—42no—
585C2×D73—42no—
586C4×C73—24no—
587C4×C73—24no—
588C4×C73—24no—
589C4×C73—42no—
590C4×C73—42no—
591C4×C73—42no—
592Dic73—24no—
593Dic73—24no—
594Dic73—24no—
595Dic73—42no—
596Dic73—42no—
597Dic73—42no—
598Dic73—42no—
599#13813—731nomaximal, Sylow
600C2×C73—28no—
601C2×C73C2×C4×C22⋊C411yescharacteristic
602C2×C73C42×D411yescharacteristic
603C2×C73#227511yescharacteristic
604C2×C73D4×C22⋊C411yescharacteristic
605C2×C73#233911yescharacteristic
606C2×C73#235211yescharacteristic
607C2×C73#235311yescharacteristic
608C2×C73#235811yescharacteristic
609C2×C73#235811yescharacteristic
610C2×C73#235911yescharacteristic
611C2×C73#235911yescharacteristic
612C2×C73#236111yescharacteristic
613C2×C73#236111yescharacteristic
614C2×C73#236411yescharacteristic
615C2×C73#236411yescharacteristic
616D73—44no—
617C22×C4×D4—731no—
618C2×#386—731no—
619C2×#386—731no—
620C2×C4×C22⋊C4—731no—
621C2×C4×C22⋊C4—731no—
622C2×C4×C22⋊C4D7311yescharacteristic, complemented
623C22×#95—731no—
624#1437—731no—
625#1437—731no—
626#1436—731no—
627#1436—731no—
628#1434—731no—
629C22⋊#95—731no—
630C22⋊#95—731no—
631C4×#95—731no—
632C73#1381311yescharacteristic, complemented, Sylow
633C23×D4—731no—
634C24×C4—731no—
635C24×C4—731no—
636C24×C4—731no—
637C24×C4C2×D7311yescharacteristic
638C2×C4×D4—738no—
639C2×C4×D4—1464no—
640C2×C4×D4—1464no—
641C22×C4⋊C4—731no—
642C22×C22⋊C4—731no—
643C22×C22⋊C4—731no—
644C22×C22⋊C4—731no—
645C22×C22⋊C4—731no—
646C22×C22⋊C4—731no—
647C22×C22⋊C4—731no—
648C22×C22⋊C4C2×D7311yescharacteristic
649C22×C22⋊C4C2×D7311yescharacteristic
650C22×C42—731no—
651C22×C42—731no—
652C22×C42—731no—
653C22×C42C2×D7311yescharacteristic
654C22×C42C2×D7311yescharacteristic
655#386—738no—
656#386—738no—
657C4×C22⋊C4—24no—
658C4×C22⋊C4—1464no—
659C4×C22⋊C4—1464no—
660C2×#95—731no—
661C2×#95—731no—
662C2×#95—731no—
663C2×#95—731no—
664C2×#95—731no—
665C2×#95—731no—
666C2×#95—731no—
667C2×#95—731no—
668C2×#95—731no—
669C2×#95—731no—
670C2×#95—731no—
671C2×#95—731no—
672C2×#95—731no—
673C2×#95—731no—
674C2×#95—1464no—
675C2×#95C2×D7311yescharacteristic
676C2×#95C2×D7311yescharacteristic
677C25—731no—
678C25C22×D7311yescharacteristic
679C22×D4—734no—
680C22×D4—734no—
681C22×D4—734no—
682C22×D4—1462no—
683C22×D4—1462no—
684C22×D4—1462no—
685C22×D4—1462no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—2921no—
693C23×C4—2921no—
694C23×C4—2921no—
695C23×C4—2921no—
696C23×C4—2921no—
697C23×C4—2921no—
698C23×C4—734no—
699C23×C4—734no—
700C23×C4—734no—
701C23×C4—731no—
702C23×C4—731no—
703C23×C4—731no—
704C23×C4—731no—
705C23×C4—731no—
706C23×C4—731no—
707C23×C4—731no—
708C23×C4—1462no—
709C23×C4—1462no—
710C23×C4—1462no—
711C23×C4—1462no—
712C23×C4—1462no—
713C23×C4—1462no—
714C23×C4—1462no—
715C23×C4—1462no—
716C23×C4—1462no—
717C23×C4—1462no—
718C23×C4—1462no—
719C23×C4—1462no—
720C23×C4C4×D7314yescomplemented
721C23×C4C22×D7311yescharacteristic
722C23×C4C22×D7311yescharacteristic
723C23×C4C22×D7311yescharacteristic
724C23×C4C22×D7311yescharacteristic
725C23×C4C22×D7311yescharacteristic
726C23×C4C22×D7311yescharacteristic
727C4×D4—14632no—
728C2×C4⋊C4—734no—
729C2×C4⋊C4—1462no—
730C2×C4⋊C4—1462no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—2921no—
734C2×C22⋊C4—2921no—
735C2×C22⋊C4—2921no—
736C2×C22⋊C4—2921no—
737C2×C22⋊C4—734no—
738C2×C22⋊C4—734no—
739C2×C22⋊C4—734no—
740C2×C22⋊C4—734no—
741C2×C22⋊C4—734no—
742C2×C22⋊C4—734no—
743C2×C22⋊C4—1462no—
744C2×C22⋊C4—1462no—
745C2×C22⋊C4—1462no—
746C2×C22⋊C4—1462no—
747C2×C22⋊C4—1462no—
748C2×C22⋊C4—1462no—
749C2×C22⋊C4—1462no—
750C2×C22⋊C4—1462no—
751C2×C22⋊C4C4×D7314yes—
752C2×C22⋊C4C4×D7314yescomplemented
753C2×C22⋊C4D29214yes—
754C2×C22⋊C4C22⋊D7314yes—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—41no—
760C2×C42—41no—
761C2×C42—2921no—
762C2×C42—2921no—
763C2×C42—734no—
764C2×C42—1462no—
765C2×C42—1462no—
766C2×C42—1462no—
767C2×C42—1462no—
768C2×C42—1462no—
769C2×C42—1462no—
770#95—22no—
771#95—22no—
772#95—2921no—
773#95—2921no—
774#95—734no—
775#95—734no—
776#95—734no—
777#95—734no—
778#95—734no—
779#95—1462no—
780#95—1462no—
781#95—1462no—
782#95—1462no—
783#95—1462no—
784#95—1462no—
785#95—1462no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—732no—
795C24—732no—
796C24—732no—
797C24—1461no—
798C24—1461no—
799C24—1461no—
800C24—1461no—
801C24—1461no—
802C24—1461no—
803C24—1461no—
804C24—1461no—
805C24—1461no—
806C24—1461no—
807C24—1461no—
808C24—1461no—
809C24C2×C4×D7312yes—
810C24C2×C4×D7312yes—
811C24C2×C4×D7312yes—
812C24C2×C22⋊D7312yes—
813C24C2×D29212yes—
814C24#1192402812yes—
815C24#1192402812yes—
816C24C23×D7311yescharacteristic
817C2×D4—7316no—
818C2×D4—1468no—
819C2×D4—1468no—
820C2×D4—1468no—
821C2×D4—1468no—
822C2×D4—1468no—
823C2×D4—1468no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—28no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—2924no—
862C22×C4—2924no—
863C22×C4—2924no—
864C22×C4—2924no—
865C22×C4—2924no—
866C22×C4—2924no—
867C22×C4—2924no—
868C22×C4—2924no—
869C22×C4—2924no—
870C22×C4—2924no—
871C22×C4—2924no—
872C22×C4—2924no—
873C22×C4—2924no—
874C22×C4—2924no—
875C22×C4—2924no—
876C22×C4—732no—
877C22×C4—732no—
878C22×C4—732no—
879C22×C4—732no—
880C22×C4—732no—
881C22×C4—732no—
882C22×C4—732no—
883C22×C4—732no—
884C22×C4—732no—
885C22×C4—732no—
886C22×C4—732no—
887C22×C4—732no—
888C22×C4—732no—
889C22×C4—1468no—
890C22×C4—1468no—
891C22×C4—1468no—
892C22×C4—1468no—
893C22×C4—1468no—
894C22×C4—1461no—
895C22×C4—1461no—
896C22×C4—1461no—
897C22×C4—1461no—
898C22×C4—1461no—
899C22×C4—1461no—
900C22×C4—1461no—
901C22×C4—1461no—
902C22×C4—1461no—
903C22×C4—1461no—
904C22×C4—1461no—
905C22×C4—1461no—
906C22×C4—1461no—
907C22×C4—1461no—
908C22×C4—1461no—
909C22×C4—1461no—
910C22×C4—1461no—
911C22×C4—1461no—
912C22×C4—1461no—
913C22×C4—1461no—
914C22×C4—1461no—
915C22×C4—1461no—
916C22×C4—1461no—
917C22×C4—1461no—
918C22×C4—1468no—
919C22×C4—1461no—
920C22×C4—1461no—
921C22×C4—1461no—
922C22×C4—1461no—
923C22×C4—1461no—
924C22×C4—1461no—
925C22×C4—1461no—
926C22×C4—1461no—
927C22×C4—1461no—
928C22×C4—1461no—
929C22×C4—1461no—
930C22×C4—1461no—
931C22×C4C2×C4×D7312yes—
932C22×C4C2×C4×D7312yes—
933C22×C4C2×C4×D7312yes—
934C22×C4C2×C4×D7312yes—
935C22×C4C2×C4×D7312yes—
936C22×C4C2×C4×D7312yes—
937C22×C4D4×D7312yes—
938C22×C4C2×C22⋊D7312yes—
939C22×C4C2×C22⋊D7312yes—
940C22×C4C2×D29212yes—
941C22×C4C2×D29212yes—
942C22×C4#1192402712yes—
943C4⋊C4—1468no—
944C22⋊C4—28no—
945C22⋊C4—2924no—
946C22⋊C4—2924no—
947C22⋊C4—1468no—
948C22⋊C4—1468no—
949C22⋊C4—1468no—
950C22⋊C4—1468no—
951C22⋊C4#11924005116yescomplemented
952C42—44no—
953C42—44no—
954C42—2924no—
955C42—2924no—
956C42—1468no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—2921no—
986C23—2921no—
987C23—2921no—
988C23—2921no—
989C23—2921no—
990C23—2921no—
991C23—2921no—
992C23—2921no—
993C23—2921no—
994C23—2921no—
995C23—2921no—
996C23—2921no—
997C23—2921no—
998C23—2921no—
999C23—2921no—
1000C23—2921no—
1001C23—734no—
1002C23—1462no—
1003C23—1462no—
1004C23—1462no—
1005C23—1462no—
1006C23—1462no—
1007C23—1462no—
1008C23—1462no—
1009C23—1462no—
1010C23—1462no—
1011C23—1462no—
1012C23—1462no—
1013C23—1462no—
1014C23—1462no—
1015C23—1462no—
1016C23—1462no—
1017C23—1462no—
1018C23—1462no—
1019C23—1462no—
1020C23C42×D7314yes—
1021C23C2×#1192400514yes—
1022C23#1455654814yes—
1023C23C4×C22⋊D7314yes—
1024C23C4×C22⋊D7314yes—
1025C23C4×D29214yes—
1026C23C4×D29214yes—
1027C23C22×C4×D7311yescharacteristic
1028C23C22×C4×D7311yescharacteristic
1029C23C22×C4×D7311yescharacteristic
1030C23C2×D4×D7311yescharacteristic
1031C23C22×C22⋊D7311yescharacteristic
1032C23C22×D29211yescharacteristic
1033C23#41×D7311yescharacteristic
1034C23#41×D7311yescharacteristic
1035C23C2×#1192402711yescharacteristic
1036C23C2×#1192402811yescharacteristic
1037C23C2×#1192402811yescharacteristic
1038C23#1455663611yescharacteristic
1039C23#1455663611yescharacteristic
1040C23#1455663711yescharacteristic
1041C23#1455663811yescharacteristic
1042D4—14632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—29216no—
1084C2×C4—2921no—
1085C2×C4—2921no—
1086C2×C4—2921no—
1087C2×C4—2921no—
1088C2×C4—2921no—
1089C2×C4—2921no—
1090C2×C4—2921no—
1091C2×C4—2921no—
1092C2×C4—2921no—
1093C2×C4—2921no—
1094C2×C4—2921no—
1095C2×C4—2921no—
1096C2×C4—2921no—
1097C2×C4—2921no—
1098C2×C4—2921no—
1099C2×C4—2921no—
1100C2×C4—29216no—
1101C2×C4—29216no—
1102C2×C4—734no—
1103C2×C4—734no—
1104C2×C4—734no—
1105C2×C4—1462no—
1106C2×C4—1462no—
1107C2×C4—1462no—
1108C2×C4—1462no—
1109C2×C4—1462no—
1110C2×C4—1462no—
1111C2×C4—1462no—
1112C2×C4—1462no—
1113C2×C4—1462no—
1114C2×C4—1462no—
1115C2×C4—1462no—
1116C2×C4—1462no—
1117C2×C4—1462no—
1118C2×C4—1462no—
1119C2×C4—1462no—
1120C2×C4—1462no—
1121C2×C4—1462no—
1122C2×C4—1462no—
1123C2×C4—1462no—
1124C2×C4—1462no—
1125C2×C4—1462no—
1126C2×C4—1462no—
1127C2×C4—1462no—
1128C2×C4—1462no—
1129C2×C4—1462no—
1130C2×C4—1462no—
1131C2×C4—1462no—
1132C2×C4—1462no—
1133C2×C4—1462no—
1134C2×C4—1462no—
1135C2×C4C2×#1192400514yes—
1136C2×C4C2×#1192400514yes—
1137C2×C4#1455655114yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—2922no—
1153C22—2922no—
1154C22—2922no—
1155C22—2922no—
1156C22—2922no—
1157C22—2922no—
1158C22—2922no—
1159C22—2922no—
1160C22—2922no—
1161C22—2922no—
1162C22—2922no—
1163C22—2922no—
1164C22—1464no—
1165C22—1464no—
1166C22—1464no—
1167C22C4×#1192400518yescomplemented
1168C22C2×C42×D7311yescharacteristic
1169C22C22×#1192400511yescharacteristic
1170C22C2×#1455654811yescharacteristic
1171C22C4×D4×D7311yescharacteristic
1172C22C4×D4×D7311yescharacteristic
1173C22C2×#1455655111yescharacteristic
1174C22C2×C4×C22⋊D7311yescharacteristic
1175C22C2×C4×C22⋊D7311yescharacteristic
1176C22C2×C4×D29211yescharacteristic
1177C22C2×C4×D29211yescharacteristic
1178C22C4×#1192402711yescharacteristic
1179C22C4×#1192402711yescharacteristic
1180C22#1798905511yescharacteristic
1181C22#1798905911yescharacteristic
1182C22#1798905911yescharacteristic
1183C22#1798906011yescharacteristic
1184C22#1798906611yescharacteristic
1185C22#1798906611yescharacteristic
1186C22#1798906711yescharacteristic
1187C22D4×C22⋊D7311yescharacteristic
1188C22D4×D29211yescharacteristic
1189C22#1798922511yescharacteristic
1190C22#1798922711yescharacteristic
1191C22#1798923111yescharacteristic
1192C22#1798923211yescharacteristic
1193C22#1798923211yescharacteristic
1194C22#1798923611yescharacteristic
1195C22#1798924111yescharacteristic
1196C22#1798924611yescharacteristic
1197C22#1798926111yescharacteristic
1198C22#1798926311yescharacteristic
1199C22#1798927011yescharacteristic
1200C22#1798928311yescharacteristic
1201C22#1798928611yescharacteristic
1202C22#1798928611yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—2922no—
1210C4—2922no—
1211C4—2922no—
1212C4—2922no—
1213C4—1464no—
1214C4—1464no—
1215C4—1464no—
1216C2—28no—
1217C2—2924no—
1218C2C2×C4×#1192400511yescharacteristic
1219C2C4×#1455655111yescharacteristic
1220C2#2261229011yescharacteristic
1221C2D4×#1192400511yescharacteristic
1222C2#2261275611yescharacteristic
1223C2#2261285411yescharacteristic
1224C2#2261286511yescharacteristic
1225C2#2261291011yescharacteristic
1226C2#2261291311yescharacteristic
1227C2#2261292311yescharacteristic
1228C2#2261292511yescharacteristic
1229C2#2261294511yescharacteristic
1230C2#2261294811yescharacteristic
1231C2#2261297611yescharacteristic
1232C2#2261298111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC2×C4×C22⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC23×C22⋊D73C22
hypercenterC2×C4×C22⋊C4D73
hypocenterC73#13813
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic73C2semidirect
5. C2×C4×#11924005C2semidirect
6. C22×#14556498C2semidirect
7. #22608169C2semidirect
8. #22608167C2semidirect
9. #22608166C2semidirect
10. #22608164C2semidirect
11. #22608155C2semidirect
12. #22608153C2semidirect
13. #22608152C2semidirect
14. C4×#14556498C2semidirect
15. C2×C4×C22⋊C4×C73C2semidirect
22. C2×#14556551C4semidirect
33. #17988466C4semidirect
34. #17988464C4semidirect
81. C23×Dic73C2×C4semidirect
95. C22×C4×D73C2×C4semidirect
99. C2×#11924007C2×C4semidirect
102. C2×C22⋊Dic73C2×C4semidirect
113. C2×#11924005C2×C4semidirect
114. C2×#11924005C2×C4semidirect
115. C2×#11924005C2×C4semidirect
116. C2×#11924005C2×C4semidirect
117. C2×#11924005C2×C4semidirect
126. C2×C4×Dic73C2×C4semidirect
136. #14556498C2×C4semidirect
137. #14556498C2×C4semidirect
138. #14556498C2×C4semidirect
139. #14556498C2×C4semidirect
140. #14556498D4semidirect
148. C23×C4×C73C2×C4semidirect
158. C2×C22⋊C4×C73C2×C4semidirect
190. C2×C22⋊D73C42semidirect
337. C22⋊C4×C73C22⋊C4semidirect
467. C2×C4×C73C4×D4semidirect
519. C2×Dic73C4×D4semidirect
535. C22×C73C4×C22⋊C4semidirect
622. C2×C4×C22⋊C4D73semidirect
632. C73#13813semidirect
720. C23×C4C4×D73semidirect
752. C2×C22⋊C4C4×D73semidirect
951. C22⋊C4#11924005semidirect
1137. C2×C4#14556551semidirect
1167. C22C4×#11924005semidirect

Maximal subgroups

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

subgroupindex
C22×#145565512
C2×#179884662
C2×#179884642
C2×C22⋊C4×Dic732
C2×C4×#119240052
C22×#145564982
#226081692
#226081672
#226081662
#226081642
#226081552
#226081532
#226081522
C4×#145564982
C2×C4×C22⋊C4×C732
#1381373