Finite Group Databasebeta

← #32992177

Subgroups — #32992177

Order 18688.

1266 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988462C211yesmaximal, characteristic
2C2×C22⋊C4×Dic73C211yesmaximal, characteristic
3C2×#17988354C211yesmaximal, characteristic
4C2×#17988353C211yesmaximal, characteristic
5C2×#17988353C211yesmaximal, characteristic
6#22608153C211yesmaximal, characteristic
7C2×#342×C73C211yesmaximal, characteristic
8C24×Dic73C2211yescharacteristic
9C22×C4⋊Dic73C412yescomplemented
10C22×C22⋊Dic73C2211yescharacteristic
11C22×C22⋊Dic73C2211yescharacteristic
12C22×C22⋊Dic73C2211yescharacteristic
13C22×C4×Dic73—21no—
14#17988462—21no—
15#17988462—22no—
16#17988462—21no—
17C22⋊C4×Dic73—22no—
18C22⋊C4×Dic73—22no—
19C2×#14556498—21no—
20C2×#14556498—22no—
21C2×#14556498C412yescomplemented
22#17988354C414yescomplemented
23#17988353—22no—
24#17988353—22no—
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊C4×C73C2211yescharacteristic
28#342×C73C414yescomplemented
29C23×Dic73—21no—
30C23×Dic73—21no—
31C23×Dic73—21no—
32C23×Dic73—21no—
33C23×Dic73—21no—
34C23×Dic73—21no—
35C23×Dic73—44no—
36C23×Dic73C2×C412yes—
37C23×Dic73C2×C411yescharacteristic
38C23×Dic73C2×C411yescharacteristic
39C23×Dic73D411yescharacteristic
40C23×Dic73D412yes—
41C23×Dic73D411yescharacteristic
42C2×C4⋊Dic73—22no—
43C2×C4⋊Dic73—22no—
44C2×C4⋊Dic73—44no—
45C2×C22⋊Dic73—21no—
46C2×C22⋊Dic73—21no—
47C2×C22⋊Dic73—21no—
48C2×C22⋊Dic73—21no—
49C2×C22⋊Dic73—21no—
50C2×C22⋊Dic73—21no—
51C2×C22⋊Dic73—21no—
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⋊Dic73C2×C412yes—
60C2×C22⋊Dic73C2×C412yes—
61C2×C22⋊Dic73D412yes—
62C2×C22⋊Dic73Q812yes—
63C2×C4×Dic73—24no—
64C2×C4×Dic73—44no—
65#14556498—24no—
66#14556498—22no—
67#14556498—22no—
68#14556498—44no—
69C25×C73C2311yescharacteristic
70C23×C4×C73—21no—
71C23×C4×C73—21no—
72C23×C4×C73C2×C412yes—
73C2×C22⋊C4×C73—21no—
74C2×C22⋊C4×C73—21no—
75C2×C22⋊C4×C73—21no—
76C2×C22⋊C4×C73—21no—
77C2×C22⋊C4×C73—21no—
78C2×C22⋊C4×C73—21no—
79C2×C22⋊C4×C73—21no—
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×C73C2×C412yes—
86C2×C22⋊C4×C73C2×C412yes—
87C2×C22⋊C4×C73C2×C412yes—
88C2×C22⋊C4×C73C2×C412yes—
89C2×C22⋊C4×C73D412yes—
90C2×C22⋊C4×C73Q812yes—
91C22×Dic73—21no—
92C22×Dic73—21no—
93C22×Dic73—24no—
94C22×Dic73—22no—
95C22×Dic73—22no—
96C22×Dic73—22no—
97C22×Dic73—21no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—22no—
101C22×Dic73—22no—
102C22×Dic73—21no—
103C22×Dic73—24no—
104C22×Dic73—24no—
105C22×Dic73—21no—
106C22×Dic73—21no—
107C22×Dic73—22no—
108C22×Dic73—21no—
109C22×Dic73—21no—
110C22×Dic73—21no—
111C22×Dic73—21no—
112C22×Dic73—42no—
113C22×Dic73—42no—
114C22×Dic73—42no—
115C22×Dic73—44no—
116C22×Dic73—44no—
117C22×Dic73—44no—
118C22×Dic73—44no—
119C22×Dic73—42no—
120C22×Dic73—42no—
121C22×Dic73—42no—
122C22×Dic73—42no—
123C22×Dic73—41no—
124C22×Dic73—41no—
125C22×Dic73—42no—
126C22×Dic73—42no—
127C22×Dic73C22⋊C412yes—
128C22×Dic73C22⋊C412yes—
129C4⋊Dic73—44no—
130C4⋊Dic73—44no—
131C22⋊Dic73—22no—
132C22⋊Dic73—22no—
133C22⋊Dic73—22no—
134C22⋊Dic73—22no—
135C22⋊Dic73—22no—
136C22⋊Dic73—41no—
137C22⋊Dic73—41no—
138C22⋊Dic73—41no—
139C22⋊Dic73—41no—
140C22⋊Dic73—41no—
141C22⋊Dic73—41no—
142C22⋊Dic73C4⋊C414yescomplemented
143C4×Dic73—48no—
144C24×C73—42no—
145C24×C73—42no—
146C24×C73C22×C411yescharacteristic
147C24×C73C22×C411yescharacteristic
148C24×C73C22×C411yescharacteristic
149C24×C73C2×D411yescharacteristic
150C24×C73C2×D411yescharacteristic
151C24×C73C2×D411yescharacteristic
152C24×C73C2×D411yescharacteristic
153C24×C73C2×Q811yescharacteristic
154C24×C73C2×Q811yescharacteristic
155C24×C73#4111yescharacteristic
156C24×C73#4111yescharacteristic
157C24×C73#4111yescharacteristic
158C24×C73#4111yescharacteristic
159C24×C73#4111yescharacteristic
160C24×C73#4111yescharacteristic
161C22×C4×C73—22no—
162C22×C4×C73—22no—
163C22×C4×C73—22no—
164C22×C4×C73—22no—
165C22×C4×C73—22no—
166C22×C4×C73—22no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—42no—
173C22×C4×C73—41no—
174C22×C4×C73—41no—
175C22×C4×C73C4214yescomplemented
176C22⋊C4×C73—22no—
177C22⋊C4×C73—22no—
178C22⋊C4×C73—22no—
179C22⋊C4×C73—22no—
180C22⋊C4×C73—22no—
181C22⋊C4×C73—22no—
182C22⋊C4×C73—22no—
183C22⋊C4×C73—22no—
184C22⋊C4×C73—22no—
185C22⋊C4×C73—41no—
186C22⋊C4×C73—41no—
187C22⋊C4×C73C4⋊C414yescomplemented
188C23×C73—22no—
189C23×C73—22no—
190C23×C73—22no—
191C23×C73—22no—
192C23×C73—22no—
193C23×C73—22no—
194C23×C73—42no—
195C23×C73—42no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73—42no—
201C23×C73—42no—
202C23×C73—42no—
203C23×C73—42no—
204C23×C73—42no—
205C23×C73—41no—
206C23×C73—42no—
207C23×C73—41no—
208C23×C73—41no—
209C23×C73—41no—
210C23×C73C2×C4211yescharacteristic
211C23×C73C2×C22⋊C411yescharacteristic
212C23×C73C2×C4⋊C411yescharacteristic
213C23×C73C2×C4⋊C411yescharacteristic
214C23×C73#11711yescharacteristic
215C23×C73#11711yescharacteristic
216C23×C73#11711yescharacteristic
217C23×C73C4×D411yescharacteristic
218C23×C73C4×D411yescharacteristic
219C23×C73C4×D411yescharacteristic
220C23×C73C4×D411yescharacteristic
221C23×C73C4×D411yescharacteristic
222C23×C73C4×D411yescharacteristic
223C23×C73C4×D411yescharacteristic
224C23×C73C4×D411yescharacteristic
225C23×C73C4×Q811yescharacteristic
226C23×C73C4×Q811yescharacteristic
227C23×C73C4×Q811yescharacteristic
228C23×C73C4×Q811yescharacteristic
229C23×C73#12011yescharacteristic
230C23×C73#12111yescharacteristic
231C23×C73#12111yescharacteristic
232C23×C73C22⋊Q811yescharacteristic
233C23×C73C22⋊Q811yescharacteristic
234C23×C73C22⋊Q811yescharacteristic
235C23×C73C22⋊Q811yescharacteristic
236C23×C73#12311yescharacteristic
237C23×C73#12311yescharacteristic
238C23×C73#12311yescharacteristic
239C23×C73#12411yescharacteristic
240C23×C73#12511yescharacteristic
241C23×C73#12511yescharacteristic
242C23×C73#12611yescharacteristic
243C23×C73#12611yescharacteristic
244C23×C73C4⋊Q811yescharacteristic
245C2×C4×C73—24no—
246C2×C4×C73—24no—
247C2×C4×C73—42no—
248C2×C4×C73—44no—
249C2×C4×C73—44no—
250C2×C4×C73—44no—
251C2×C4×C73—42no—
252C2×C4×C73—42no—
253C2×C4×C73—42no—
254C2×C4×C73—44no—
255C2×C4×C73—44no—
256C2×C4×C73—42no—
257C2×C4×C73—81no—
258C2×C4×C73—81no—
259C2×C4×C73—82no—
260C2×Dic73—24no—
261C2×Dic73—24no—
262C2×Dic73—22no—
263C2×Dic73—22no—
264C2×Dic73—24no—
265C2×Dic73—22no—
266C2×Dic73—22no—
267C2×Dic73—22no—
268C2×Dic73—44no—
269C2×Dic73—44no—
270C2×Dic73—44no—
271C2×Dic73—44no—
272C2×Dic73—42no—
273C2×Dic73—42no—
274C2×Dic73—44no—
275C2×Dic73—44no—
276C2×Dic73—42no—
277C2×Dic73—42no—
278C2×Dic73—44no—
279C2×Dic73—41no—
280C2×Dic73—41no—
281C2×Dic73—42no—
282C2×Dic73—42no—
283C2×Dic73—42no—
284C2×Dic73—81no—
285C2×Dic73—81no—
286C2×Dic73—82no—
287C2×Dic73—81no—
288C2×Dic73—81no—
289C2×Dic73—81no—
290C2×Dic73—81no—
291C2×Dic73#9914yes—
292C22×C73—21no—
293C22×C73—21no—
294C22×C73—21no—
295C22×C73—21no—
296C22×C73—21no—
297C22×C73—21no—
298C22×C73—21no—
299C22×C73—21no—
300C22×C73—21no—
301C22×C73—21no—
302C22×C73—21no—
303C22×C73—21no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73C4×C22⋊C411yescharacteristic
333C22×C73C4×C4⋊C411yescharacteristic
334C22×C73C4×C4⋊C411yescharacteristic
335C22×C73#38511yescharacteristic
336C22×C73#38511yescharacteristic
337C22×C73#38611yescharacteristic
338C22×C73#38711yescharacteristic
339C22×C73#38711yescharacteristic
340C22×C73#38711yescharacteristic
341C22×C73#38711yescharacteristic
342C22×C73#38811yescharacteristic
343C22×C73#38811yescharacteristic
344C22×C73#38911yescharacteristic
345C22×C73#38911yescharacteristic
346C22×C73#39111yescharacteristic
347C22×C73C2×#9912yes—
348C22×C73#41012yes—
349C4×C73—44no—
350C4×C73—44no—
351C4×C73—82no—
352Dic73—24no—
353Dic73—44no—
354Dic73—42no—
355Dic73—82no—
356Dic73—81no—
357Dic73—81no—
358#10912—731nomaximal, Sylow
359C2×C73—21no—
360C2×C73—21no—
361C2×C73—21no—
362C2×C73—21no—
363C2×C73—21no—
364C2×C73—21no—
365C2×C73—21no—
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—21no—
369C2×C73—21no—
370C2×C73—21no—
371C2×C73#143611yescharacteristic
372C2×C73C4×#9912yes—
373C2×C73#189811yescharacteristic
374C2×C73#189911yescharacteristic
375C2×C73#199612yes—
376C2×#385—731no—
377C2×C4×C22⋊C4—731no—
378C2×#342—731no—
379C2×#342—731no—
380C2×#342—731no—
381C2×#342D7311yescharacteristic
382C22⋊#95—731no—
383C73#1091211yescharacteristic, complemented, Sylow
384C24×C4—731no—
385C22×C4⋊C4—732no—
386C22×C22⋊C4—731no—
387C22×C22⋊C4—731no—
388C22×C22⋊C4—731no—
389C22×C22⋊C4C2×D7311yescharacteristic
390C22×C22⋊C4C2×D7311yescharacteristic
391C22×C22⋊C4C2×D7311yescharacteristic
392C22×C42—1461no—
393#385—1461no—
394#385—1462no—
395#385—1461no—
396C4×C22⋊C4—1462no—
397C4×C22⋊C4—1462no—
398C2×#95—732no—
399C2×#95—1462no—
400C2×#95—1461no—
401#342—734no—
402#342—1462no—
403#342—1462no—
404#342Dic7314yescomplemented
405C25C22×D7311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—2924no—
409C23×C4—731no—
410C23×C4—731no—
411C23×C4—731no—
412C23×C4—732no—
413C23×C4—732no—
414C23×C4—731no—
415C23×C4—1461no—
416C23×C4—1461no—
417C23×C4—1461no—
418C23×C4—1461no—
419C23×C4—1461no—
420C23×C4—1461no—
421C23×C4C4×D7312yes—
422C2×C4⋊C4—2924no—
423C2×C4⋊C4—1462no—
424C2×C4⋊C4—1462no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—732no—
438C2×C22⋊C4—732no—
439C2×C22⋊C4—732no—
440C2×C22⋊C4—732no—
441C2×C22⋊C4—1461no—
442C2×C22⋊C4—1461no—
443C2×C22⋊C4—1461no—
444C2×C22⋊C4—1461no—
445C2×C22⋊C4—1461no—
446C2×C22⋊C4—1461no—
447C2×C22⋊C4—1461no—
448C2×C22⋊C4—1461no—
449C2×C22⋊C4—1461no—
450C2×C22⋊C4—1461no—
451C2×C22⋊C4—1461no—
452C2×C22⋊C4—1461no—
453C2×C22⋊C4—1461no—
454C2×C22⋊C4—1461no—
455C2×C22⋊C4Dic14612yes—
456C2×C22⋊C4C4×D7312yes—
457C2×C22⋊C4D29212yes—
458C2×C22⋊C4C2×Dic7312yes—
459C2×C22⋊C4C2×Dic7312yes—
460C2×C22⋊C4C2×Dic7312yes—
461C2×C42—2924no—
462C2×C42—1464no—
463#95—2924no—
464#95—1462no—
465#95—1462no—
466#95—1464no—
467C24—42no—
468C24—42no—
469C24C2×C4×D7311yescharacteristic
470C24C2×C4×D7311yescharacteristic
471C24C22×Dic7311yescharacteristic
472C24D4×D7311yescharacteristic
473C24D4×D7311yescharacteristic
474C24D4×D7311yescharacteristic
475C24C2×D29211yescharacteristic
476C24Q8×D7311yescharacteristic
477C24C2×Dic14611yescharacteristic
478C24#1192402711yescharacteristic
479C24#1192402711yescharacteristic
480C24#1192402711yescharacteristic
481C24#1192402811yescharacteristic
482C24#1192402811yescharacteristic
483C24#1192402911yescharacteristic
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—2922no—
499C22×C4—2922no—
500C22×C4—2924no—
501C22×C4—2924no—
502C22×C4—2924no—
503C22×C4—2924no—
504C22×C4—2922no—
505C22×C4—2922no—
506C22×C4—2922no—
507C22×C4—2922no—
508C22×C4—2922no—
509C22×C4—2921no—
510C22×C4—2921no—
511C22×C4—2922no—
512C22×C4—2922no—
513C22×C4—732no—
514C22×C4—732no—
515C22×C4—1461no—
516C22×C4—1461no—
517C22×C4—1462no—
518C22×C4—1464no—
519C22×C4—1464no—
520C22×C4—1462no—
521C22×C4—1462no—
522C22×C4—1462no—
523C22×C4—1461no—
524C22×C4—1462no—
525C22×C4—1462no—
526C22×C4—1462no—
527C22×C4—1462no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1464no—
534C22×C4—1461no—
535C22×C4—1461no—
536C22×C4C4×Dic7314yescomplemented
537C4⋊C4—2924no—
538C4⋊C4—2924no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—2921no—
551C22⋊C4—2921no—
552C22⋊C4—2921no—
553C22⋊C4—2921no—
554C22⋊C4—2921no—
555C22⋊C4—2921no—
556C22⋊C4—734no—
557C22⋊C4—1462no—
558C22⋊C4—1462no—
559C22⋊C4—1462no—
560C22⋊C4—1462no—
561C22⋊C4—1462no—
562C22⋊C4C4⋊Dic7314yescomplemented
563C42—2928no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—42no—
575C23—42no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—41no—
584C23—42no—
585C23—41no—
586C23C2×C4×Dic7311yescharacteristic
587C23C22⋊C4×D7311yescharacteristic
588C23C4⋊C4×D7311yescharacteristic
589C23C2×C4⋊Dic7311yescharacteristic
590C23#1455654711yescharacteristic
591C23#1455654911yescharacteristic
592C23#1455655011yescharacteristic
593C23#1455655111yescharacteristic
594C23#1455655111yescharacteristic
595C23#1455655311yescharacteristic
596C23D4×Dic7311yescharacteristic
597C23D4×Dic7311yescharacteristic
598C23D4×Dic7311yescharacteristic
599C23C4×D29211yescharacteristic
600C23C4×D29211yescharacteristic
601C23#1455655611yescharacteristic
602C23C4×Dic14611yescharacteristic
603C23C4×Dic14611yescharacteristic
604C23Q8×Dic7311yescharacteristic
605C23#1455656111yescharacteristic
606C23#1455656411yescharacteristic
607C23#1455656611yescharacteristic
608C23#1455656811yescharacteristic
609C23#1455656811yescharacteristic
610C23#1455656911yescharacteristic
611C23#1455657111yescharacteristic
612C23#1455657311yescharacteristic
613C23#1455657511yescharacteristic
614C23#1455657611yescharacteristic
615C23#1455657711yescharacteristic
616C23#1455658111yescharacteristic
617C23#1455658211yescharacteristic
618C23#1455658411yescharacteristic
619C23#1455658611yescharacteristic
620C23#1455659011yescharacteristic
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—42no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—42no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—82no—
636C2×C4—2922no—
637C2×C4—2922no—
638C2×C4—2922no—
639C2×C4—2924no—
640C2×C4—2922no—
641C2×C4—2924no—
642C2×C4—2924no—
643C2×C4—2924no—
644C2×C4—2924no—
645C2×C4—2924no—
646C2×C4—2924no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—2922no—
650C2×C4—2922no—
651C2×C4—2922no—
652C2×C4—5841no—
653C2×C4—5841no—
654C2×C4—5842no—
655C2×C4—5841no—
656C2×C4—5841no—
657C2×C4—5841no—
658C2×C4—5841no—
659C2×C4—734no—
660C2×C4—1464no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1464no—
665C2×C4—1464no—
666C2×C4—1462no—
667C2×C4—1462no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22C22⋊C4×Dic7311yescharacteristic
709C22C4×C4⋊Dic7311yescharacteristic
710C22C4⋊C4×Dic7311yescharacteristic
711C22#1798846111yescharacteristic
712C22#1798846211yescharacteristic
713C22#1798846511yescharacteristic
714C22#1798847011yescharacteristic
715C22#1798847211yescharacteristic
716C22#1798847311yescharacteristic
717C22#1798847411yescharacteristic
718C22#1798847911yescharacteristic
719C22#1798848011yescharacteristic
720C22#1798848411yescharacteristic
721C22#1798848611yescharacteristic
722C22#1798849111yescharacteristic
723C22#99×D7312yes—
724C22#1798855912yes—
725C4—44no—
726C4—44no—
727C4—82no—
728C4—2924no—
729C4—2922no—
730C4—5842no—
731C4—5841no—
732C4—5841no—
733C4—1464no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2—21no—
743C2—21no—
744C2—21no—
745C2—21no—
746C2#2260816511yescharacteristic
747C2#99×Dic7312yes—
748C2#2261038311yescharacteristic
749C2#2261038811yescharacteristic
750C2#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#10912
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
9. C22×C4⋊Dic73C4semidirect
21. C2×#14556498C4semidirect
22. #17988354C4semidirect
28. #342×C73C4semidirect
142. C22⋊Dic73C4⋊C4semidirect
175. C22×C4×C73C42semidirect
187. C22⋊C4×C73C4⋊C4semidirect
383. C73#10912semidirect
404. #342Dic73semidirect
536. C22×C4C4×Dic73semidirect
562. C22⋊C4C4⋊Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884622
C2×C22⋊C4×Dic732
C2×#179883542
C2×#179883532
#226081532
C2×#342×C732
#1091273