Finite Group Databasebeta

← #32991847

Subgroups — #32991847

Order 18688.

1338 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988445C211yesmaximal, characteristic
2C2×#17988445C211yesmaximal, characteristic
3C2×C22⋊C4×Dic73C211yesmaximal, characteristic
4C2×#17988354C211yesmaximal, characteristic
5C2×#17988353C211yesmaximal, characteristic
6C2×#17988353C211yesmaximal, characteristic
7C2×#342×C73C211yesmaximal, characteristic
8C24×Dic73C2211yescharacteristic
9C22×#11924007—21no—
10C22×#11924007C412yescomplemented
11C22×C22⋊Dic73C2211yescharacteristic
12C22×C22⋊Dic73C2211yescharacteristic
13C22×C22⋊Dic73C2211yescharacteristic
14C22×C4×Dic73—21no—
15#17988445—22no—
16#17988445—21no—
17#17988445—21no—
18#17988445—21no—
19#17988445—21no—
20#17988445C414yescomplemented
21C22⋊C4×Dic73—22no—
22C22⋊C4×Dic73C414yescomplemented
23C2×#14556498—21no—
24C2×#14556498—21no—
25C2×#14556498C412yescomplemented
26#17988354—22no—
27#17988353—22no—
28#17988353—22no—
29C22×C22⋊C4×C73C2211yescharacteristic
30C22×C22⋊C4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32#342×C73—22no—
33C23×Dic73—21no—
34C23×Dic73—21no—
35C23×Dic73—44no—
36C23×Dic73C2×C411yescharacteristic
37C23×Dic73C2×C412yes—
38C23×Dic73C2×C411yescharacteristic
39C23×Dic73C2×C412yes—
40C23×Dic73C2×C412yes—
41C23×Dic73D411yescharacteristic
42C23×Dic73D411yescharacteristic
43C23×Dic73D411yescharacteristic
44C23×Dic73D411yescharacteristic
45C23×Dic73D412yes—
46C23×Dic73Q812yes—
47C2×#11924007—22no—
48C2×#11924007—22no—
49C2×#11924007—24no—
50C2×#11924007—44no—
51C2×#11924007—44no—
52C2×C22⋊Dic73—21no—
53C2×C22⋊Dic73—21no—
54C2×C22⋊Dic73—21no—
55C2×C22⋊Dic73—21no—
56C2×C22⋊Dic73—21no—
57C2×C22⋊Dic73—21no—
58C2×C22⋊Dic73—21no—
59C2×C22⋊Dic73—21no—
60C2×C22⋊Dic73—21no—
61C2×C22⋊Dic73—21no—
62C2×C22⋊Dic73—21no—
63C2×C22⋊Dic73—21no—
64C2×C22⋊Dic73—21no—
65C2×C22⋊Dic73—21no—
66C2×C22⋊Dic73C2×C412yes—
67C2×C22⋊Dic73C2×C412yes—
68C2×C22⋊Dic73D412yes—
69C2×C22⋊Dic73Q812yes—
70C2×C4×Dic73—24no—
71C2×C4×Dic73—44no—
72#14556498—24no—
73#14556498—24no—
74#14556498—22no—
75#14556498—22no—
76C25×C73C2311yescharacteristic
77C23×C4×C73—21no—
78C23×C4×C73—21no—
79C23×C4×C73C2×C412yes—
80C2×C22⋊C4×C73—21no—
81C2×C22⋊C4×C73—21no—
82C2×C22⋊C4×C73—21no—
83C2×C22⋊C4×C73—21no—
84C2×C22⋊C4×C73—21no—
85C2×C22⋊C4×C73—21no—
86C2×C22⋊C4×C73—21no—
87C2×C22⋊C4×C73—21no—
88C2×C22⋊C4×C73—21no—
89C2×C22⋊C4×C73—21no—
90C2×C22⋊C4×C73—21no—
91C2×C22⋊C4×C73—21no—
92C2×C22⋊C4×C73—21no—
93C2×C22⋊C4×C73—21no—
94C2×C22⋊C4×C73C2×C412yes—
95C2×C22⋊C4×C73C2×C412yes—
96C2×C22⋊C4×C73D412yes—
97C2×C22⋊C4×C73Q812yes—
98C22×Dic73—24no—
99C22×Dic73—24no—
100C22×Dic73—24no—
101C22×Dic73—22no—
102C22×Dic73—22no—
103C22×Dic73—22no—
104C22×Dic73—22no—
105C22×Dic73—22no—
106C22×Dic73—22no—
107C22×Dic73—22no—
108C22×Dic73—44no—
109C22×Dic73—44no—
110C22×Dic73—44no—
111C22×Dic73—44no—
112C22×Dic73—42no—
113C22×Dic73—42no—
114C22×Dic73—42no—
115C22×Dic73—42no—
116C22×Dic73—42no—
117C22×Dic73—42no—
118C22×Dic73—42no—
119C22×Dic73—41no—
120C22×Dic73—41no—
121C22×Dic73—42no—
122C22×Dic73—42no—
123C22×Dic73C4212yes—
124C22×Dic73C4212yes—
125C22×Dic73C22⋊C411yescharacteristic
126C22×Dic73C22⋊C411yescharacteristic
127C22×Dic73C22⋊C412yes—
128C22×Dic73C22⋊C412yes—
129C22×Dic73C22⋊C411yescharacteristic
130C22×Dic73C22⋊C412yes—
131C22×Dic73C22⋊C412yes—
132C22×Dic73C22⋊C411yescharacteristic
133C22×Dic73C4⋊C412yes—
134C22×Dic73C4⋊C412yes—
135C22×Dic73C4⋊C412yes—
136C22×Dic73C4⋊C412yes—
137C22×Dic73C4⋊C412yes—
138C22×Dic73C4⋊C412yes—
139#11924007—44no—
140#11924007—48no—
141#11924007—44no—
142C22⋊Dic73—22no—
143C22⋊Dic73—22no—
144C22⋊Dic73—22no—
145C22⋊Dic73—22no—
146C22⋊Dic73—22no—
147C22⋊Dic73—41no—
148C22⋊Dic73—41no—
149C22⋊Dic73—41no—
150C22⋊Dic73—41no—
151C22⋊Dic73—41no—
152C22⋊Dic73—41no—
153C22⋊Dic73C4⋊C414yescomplemented
154C4×Dic73—48no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73C22×C411yescharacteristic
158C24×C73C22×C411yescharacteristic
159C24×C73C22×C411yescharacteristic
160C24×C73C2×D411yescharacteristic
161C24×C73C2×D411yescharacteristic
162C24×C73C2×D411yescharacteristic
163C24×C73C2×D411yescharacteristic
164C24×C73C2×D411yescharacteristic
165C24×C73C2×Q811yescharacteristic
166C24×C73C2×Q811yescharacteristic
167C24×C73C2×Q811yescharacteristic
168C24×C73#4111yescharacteristic
169C24×C73#4111yescharacteristic
170C24×C73#4111yescharacteristic
171C24×C73#4111yescharacteristic
172C22×C4×C73—22no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—42no—
180C22×C4×C73—42no—
181C22×C4×C73—42no—
182C22×C4×C73—42no—
183C22×C4×C73—41no—
184C22×C4×C73—41no—
185C22×C4×C73—42no—
186C22×C4×C73—42no—
187C22⋊C4×C73—22no—
188C22⋊C4×C73—22no—
189C22⋊C4×C73—22no—
190C22⋊C4×C73—22no—
191C22⋊C4×C73—22no—
192C22⋊C4×C73—41no—
193C22⋊C4×C73—41no—
194C22⋊C4×C73—41no—
195C22⋊C4×C73—41no—
196C22⋊C4×C73—41no—
197C22⋊C4×C73—41no—
198C22⋊C4×C73C4⋊C414yescomplemented
199C23×C73—22no—
200C23×C73—22no—
201C23×C73—22no—
202C23×C73—22no—
203C23×C73—22no—
204C23×C73—22no—
205C23×C73—41no—
206C23×C73—41no—
207C23×C73—41no—
208C23×C73—41no—
209C23×C73—42no—
210C23×C73—41no—
211C23×C73—42no—
212C23×C73—41no—
213C23×C73—41no—
214C23×C73—42no—
215C23×C73—42no—
216C23×C73—41no—
217C23×C73—42no—
218C23×C73—42no—
219C23×C73—42no—
220C23×C73—42no—
221C23×C73C2×C4211yescharacteristic
222C23×C73C2×C22⋊C411yescharacteristic
223C23×C73C2×C22⋊C411yescharacteristic
224C23×C73C2×C22⋊C411yescharacteristic
225C23×C73C2×C4⋊C411yescharacteristic
226C23×C73C2×C4⋊C411yescharacteristic
227C23×C73C2×C4⋊C411yescharacteristic
228C23×C73C2×C4⋊C411yescharacteristic
229C23×C73C2×C4⋊C411yescharacteristic
230C23×C73#11711yescharacteristic
231C23×C73#11711yescharacteristic
232C23×C73C4×D411yescharacteristic
233C23×C73C4×D411yescharacteristic
234C23×C73C4×D411yescharacteristic
235C23×C73C4×D411yescharacteristic
236C23×C73C4×Q811yescharacteristic
237C23×C73C4×Q811yescharacteristic
238C23×C73C4×Q811yescharacteristic
239C23×C73C4×Q811yescharacteristic
240C23×C73#12111yescharacteristic
241C23×C73#12111yescharacteristic
242C23×C73#12111yescharacteristic
243C23×C73#12111yescharacteristic
244C23×C73C22⋊Q811yescharacteristic
245C23×C73C22⋊Q811yescharacteristic
246C23×C73C22⋊Q811yescharacteristic
247C23×C73C22⋊Q811yescharacteristic
248C23×C73#12411yescharacteristic
249C23×C73#12411yescharacteristic
250C23×C73#12511yescharacteristic
251C23×C73#12511yescharacteristic
252C23×C73#12711yescharacteristic
253C23×C73C4⋊Q811yescharacteristic
254C23×C73C4⋊Q811yescharacteristic
255C23×C73C4⋊Q811yescharacteristic
256C2×C4×C73—24no—
257C2×C4×C73—44no—
258C2×C4×C73—42no—
259C2×C4×C73—44no—
260C2×C4×C73—42no—
261C2×C4×C73—42no—
262C2×C4×C73—42no—
263C2×C4×C73—42no—
264C2×C4×C73—42no—
265C2×C4×C73—42no—
266C2×C4×C73—42no—
267C2×C4×C73—82no—
268C2×C4×C73—82no—
269C2×C4×C73—82no—
270C2×C4×C73—82no—
271C2×Dic73—22no—
272C2×Dic73—22no—
273C2×Dic73—22no—
274C2×Dic73—24no—
275C2×Dic73—24no—
276C2×Dic73—24no—
277C2×Dic73—24no—
278C2×Dic73—24no—
279C2×Dic73—24no—
280C2×Dic73—24no—
281C2×Dic73—42no—
282C2×Dic73—42no—
283C2×Dic73—42no—
284C2×Dic73—42no—
285C2×Dic73—42no—
286C2×Dic73—42no—
287C2×Dic73—42no—
288C2×Dic73—44no—
289C2×Dic73—42no—
290C2×Dic73—44no—
291C2×Dic73—42no—
292C2×Dic73—42no—
293C2×Dic73—42no—
294C2×Dic73—42no—
295C2×Dic73—42no—
296C2×Dic73—42no—
297C2×Dic73—82no—
298C2×Dic73—82no—
299C2×Dic73—82no—
300C2×Dic73—82no—
301C2×Dic73#9512yes—
302C2×Dic73#9512yes—
303C2×Dic73#9512yes—
304C2×Dic73#9512yes—
305C2×Dic73#9914yes—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—21no—
313C22×C73—21no—
314C22×C73—21no—
315C22×C73—21no—
316C22×C73—21no—
317C22×C73—21no—
318C22×C73—21no—
319C22×C73—21no—
320C22×C73—21no—
321C22×C73—21no—
322C22×C73—21no—
323C22×C73—21no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73C2×#9511yescharacteristic
347C22×C73C4×C4⋊C411yescharacteristic
348C22×C73C4×C4⋊C411yescharacteristic
349C22×C73#38011yescharacteristic
350C22×C73#38011yescharacteristic
351C22×C73#38211yescharacteristic
352C22×C73#38411yescharacteristic
353C22×C73#38911yescharacteristic
354C22×C73#38911yescharacteristic
355C22×C73#38911yescharacteristic
356C22×C73#38911yescharacteristic
357C22×C73#39011yescharacteristic
358C22×C73#39011yescharacteristic
359C22×C73#39111yescharacteristic
360C22×C73#39111yescharacteristic
361C22×C73C2×#9912yes—
362C22×C73#41012yes—
363C4×C73—44no—
364C4×C73—82no—
365C4×C73—82no—
366Dic73—22no—
367Dic73—22no—
368Dic73—22no—
369Dic73—44no—
370Dic73—82no—
371Dic73—82no—
372Dic73#34214yescomplemented
373#10854—731nomaximal, Sylow
374C2×C73—21no—
375C2×C73—21no—
376C2×C73—21no—
377C2×C73—21no—
378C2×C73—21no—
379C2×C73—21no—
380C2×C73—21no—
381C2×C73—21no—
382C2×C73—21no—
383C2×C73—21no—
384C2×C73—21no—
385C2×C73—21no—
386C2×C73C4⋊#9511yescharacteristic
387C2×C73C2×#34211yescharacteristic
388C2×C73#174011yescharacteristic
389C2×C73#196412yes—
390C2×C73#199612yes—
391C2×#380—731no—
392C2×#380—731no—
393C2×C4×C22⋊C4—731no—
394C2×#342—731no—
395C2×#342—731no—
396C2×#342—731no—
397C2×#342D7311yescharacteristic
398C73#1085411yescharacteristic, complemented, Sylow
399C24×C4—731no—
400C22×C4⋊C4—732no—
401C22×C4⋊C4—1461no—
402C22×C22⋊C4—731no—
403C22×C22⋊C4—731no—
404C22×C22⋊C4—731no—
405C22×C22⋊C4C2×D7311yescharacteristic
406C22×C22⋊C4C2×D7311yescharacteristic
407C22×C22⋊C4C2×D7311yescharacteristic
408C22×C42—1461no—
409#380—734no—
410#380—1461no—
411#380—1461no—
412#380—1461no—
413#380—1461no—
414#380—1462no—
415C4×C22⋊C4—734no—
416C4×C22⋊C4—1462no—
417C2×#95—732no—
418C2×#95—1461no—
419C2×#95—1461no—
420#342—22no—
421#342—1462no—
422#342—1462no—
423#342—1462no—
424C25C22×D7311yescharacteristic
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—2924no—
428C23×C4—731no—
429C23×C4—732no—
430C23×C4—732no—
431C23×C4—731no—
432C23×C4—731no—
433C23×C4—732no—
434C23×C4—732no—
435C23×C4—732no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4—731no—
439C23×C4—1461no—
440C23×C4—1461no—
441C23×C4C4×D7312yes—
442C2×C4⋊C4—2924no—
443C2×C4⋊C4—2924no—
444C2×C4⋊C4—1462no—
445C2×C4⋊C4—1462no—
446C2×C4⋊C4—1464no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—732no—
462C2×C22⋊C4—732no—
463C2×C22⋊C4—732no—
464C2×C22⋊C4—732no—
465C2×C22⋊C4—1461no—
466C2×C22⋊C4—1461no—
467C2×C22⋊C4—1461no—
468C2×C22⋊C4—1461no—
469C2×C22⋊C4—1461no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4—1461no—
472C2×C22⋊C4—1461no—
473C2×C22⋊C4—1461no—
474C2×C22⋊C4—1461no—
475C2×C22⋊C4—1461no—
476C2×C22⋊C4—1461no—
477C2×C22⋊C4—1461no—
478C2×C22⋊C4—1461no—
479C2×C22⋊C4Dic14612yes—
480C2×C22⋊C4C4×D7312yes—
481C2×C22⋊C4C4×D7312yes—
482C2×C22⋊C4C22⋊D7312yes—
483C2×C42—2924no—
484C2×C42—1464no—
485#95—1462no—
486#95—1462no—
487#95—1464no—
488#95—1464no—
489C24—42no—
490C24—42no—
491C24C2×C4×D7311yescharacteristic
492C24C2×C4×D7311yescharacteristic
493C24C2×C4×D7311yescharacteristic
494C24D4×D7311yescharacteristic
495C24D4×D7311yescharacteristic
496C24D4×D7311yescharacteristic
497C24D4×D7311yescharacteristic
498C24C2×C22⋊D7311yescharacteristic
499C24Q8×D7311yescharacteristic
500C24Q8×D7311yescharacteristic
501C24C2×Dic14611yescharacteristic
502C24#1192402711yescharacteristic
503C24#1192402711yescharacteristic
504C24#1192402811yescharacteristic
505C24#1192402811yescharacteristic
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—2922no—
522C22×C4—2922no—
523C22×C4—2922no—
524C22×C4—2922no—
525C22×C4—2922no—
526C22×C4—2924no—
527C22×C4—2924no—
528C22×C4—2924no—
529C22×C4—2924no—
530C22×C4—2922no—
531C22×C4—2922no—
532C22×C4—2921no—
533C22×C4—2921no—
534C22×C4—2922no—
535C22×C4—2922no—
536C22×C4—732no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—732no—
540C22×C4—732no—
541C22×C4—732no—
542C22×C4—731no—
543C22×C4—732no—
544C22×C4—732no—
545C22×C4—732no—
546C22×C4—731no—
547C22×C4—731no—
548C22×C4—731no—
549C22×C4—732no—
550C22×C4—732no—
551C22×C4—732no—
552C22×C4—1462no—
553C22×C4—1462no—
554C22×C4—1462no—
555C22×C4—1462no—
556C22×C4—1462no—
557C22×C4—1462no—
558C22×C4—1462no—
559C22×C4—1464no—
560C22×C4—1464no—
561C22×C4—1464no—
562C4⋊C4—2924no—
563C4⋊C4—2928no—
564C4⋊C4—2924no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—2921no—
577C22⋊C4—2921no—
578C22⋊C4—2921no—
579C22⋊C4—2921no—
580C22⋊C4—2921no—
581C22⋊C4—2921no—
582C22⋊C4—734no—
583C22⋊C4—1462no—
584C22⋊C4—1462no—
585C22⋊C4—1462no—
586C22⋊C4—1462no—
587C22⋊C4—1462no—
588C22⋊C4#1192400714yescomplemented
589C42—2928no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23C42×D7311yescharacteristic
613C23C22⋊C4×D7311yescharacteristic
614C23C22⋊C4×D7311yescharacteristic
615C23C22⋊C4×D7311yescharacteristic
616C23C4⋊C4×D7311yescharacteristic
617C23C4⋊C4×D7311yescharacteristic
618C23C4⋊C4×D7311yescharacteristic
619C23C4⋊C4×D7311yescharacteristic
620C23C2×#1192400711yescharacteristic
621C23#1455654711yescharacteristic
622C23#1455654811yescharacteristic
623C23#1455655111yescharacteristic
624C23#1455655111yescharacteristic
625C23C4×C22⋊D7311yescharacteristic
626C23C4×C22⋊D7311yescharacteristic
627C23#1455655611yescharacteristic
628C23#1455655611yescharacteristic
629C23C4×Dic14611yescharacteristic
630C23C4×Dic14611yescharacteristic
631C23#1455656311yescharacteristic
632C23#1455656311yescharacteristic
633C23#1455656411yescharacteristic
634C23#1455656411yescharacteristic
635C23#1455656811yescharacteristic
636C23#1455656811yescharacteristic
637C23#1455656911yescharacteristic
638C23#1455656911yescharacteristic
639C23#1455657711yescharacteristic
640C23#1455657711yescharacteristic
641C23#1455658111yescharacteristic
642C23#1455658111yescharacteristic
643C23#1455658711yescharacteristic
644C23#1455658911yescharacteristic
645C23#1455659011yescharacteristic
646C23#1455659011yescharacteristic
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—2922no—
663C2×C4—2924no—
664C2×C4—2924no—
665C2×C4—2922no—
666C2×C4—2922no—
667C2×C4—2922no—
668C2×C4—2922no—
669C2×C4—2922no—
670C2×C4—2922no—
671C2×C4—2922no—
672C2×C4—2922no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—2922no—
677C2×C4—2922no—
678C2×C4—5842no—
679C2×C4—5842no—
680C2×C4—5842no—
681C2×C4—5842no—
682C2×C4—732no—
683C2×C4—734no—
684C2×C4—732no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—1464no—
688C2×C4—1464no—
689C2×C4—1464no—
690C2×C4—1464no—
691C2×C4—1464no—
692C2×C4—1464no—
693C2×C4—1464no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#95×D7311yescharacteristic
738C22#1798843811yescharacteristic
739C22C4×#1192400711yescharacteristic
740C22#1798844511yescharacteristic
741C22#1798844611yescharacteristic
742C22#1798845111yescharacteristic
743C22#1798845611yescharacteristic
744C22#1798848211yescharacteristic
745C22#1798848211yescharacteristic
746C22#1798848411yescharacteristic
747C22#1798848411yescharacteristic
748C22#1798848711yescharacteristic
749C22#1798848711yescharacteristic
750C22#1798849111yescharacteristic
751C22#1798849111yescharacteristic
752C22#99×D7312yes—
753C22#1798855912yes—
754C4—44no—
755C4—82no—
756C4—82no—
757C4—2924no—
758C4—5842no—
759C4—5842no—
760C4—734no—
761C4—1462no—
762C4—1462no—
763C4—1462no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2#2260815911yescharacteristic
777C2#342×D7311yescharacteristic
778C2#2260966211yescharacteristic
779C2#2261076512yes—
780C2#2261091412yes—
subgroupG/H
centerC23C22⋊C4×D73
commutatorC23×C73C2×C42
FrattiniC25C22×D73
FittingC2×#342×C73C2
socleC23×C73C2×C22⋊C4
prime radical, cosocleC25×C73C23
hypercenterC2×#342D73
hypocenterC73#10854
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
10. C22×#11924007C4semidirect
20. #17988445C4semidirect
22. C22⋊C4×Dic73C4semidirect
25. C2×#14556498C4semidirect
153. C22⋊Dic73C4⋊C4semidirect
198. C22⋊C4×C73C4⋊C4semidirect
372. Dic73#342semidirect
398. C73#10854semidirect
588. C22⋊C4#11924007semidirect

Maximal subgroups

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

subgroupindex
C2×#179884452
C2×C22⋊C4×Dic732
C2×#179883542
C2×#179883532
C2×#342×C732
#1085473