Finite Group Databasebeta

← #32993225

Subgroups — #32993225

Order 18688.

1230 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556522C211yesmaximal, characteristic, complemented
2C22×#14556503C211yesmaximal, characteristic
3C2×#17988444C211yesmaximal, characteristic
4C2×#17988444C211yesmaximal, characteristic
5C2×#17988350C211yesmaximal, characteristic, complemented
6C2×#17988349C211yesmaximal, characteristic, complemented
7C2×#340×C73C211yesmaximal, characteristic, complemented
8C23×C4×D73C2211yescharacteristic
9C23×#10596831C2211yescharacteristic
10C22×C4⋊Dic73C2211yescharacteristic
11C22×C4⋊Dic73C2211yescharacteristic
12C22×#11924005—21no—
13C22×#11924005—21no—
14C2×#14556522—22no—
15C2×#14556522—22no—
16C2×#14556522—22no—
17C2×#14556503—22no—
18C2×#14556503—22no—
19C2×#14556503C414yescomplemented
20#17988444—22no—
21#17988444—22no—
22#17988444—22no—
23#17988444—22no—
24C2×#14556498—21no—
25C2×#14556498—21no—
26#17988350—22no—
27#17988349—22no—
28C23×C8×C73C2211yescharacteristic
29C22×C4⋊C4×C73C2211yescharacteristic
30C22×C4⋊C4×C73C2211yescharacteristic
31#340×C73—22no—
32C24×D73D411yescharacteristic
33C23×Dic73—21no—
34C23×Dic73—21no—
35C23×Dic73D411yescharacteristic
36C22×C4×D73—21no—
37C22×C4×D73—21no—
38C22×C4×D73—21no—
39C22×C4×D73—21no—
40C22×C4×D73—21no—
41C22×C4×D73—21no—
42C22×C4×D73—21no—
43C22×C4×D73—21no—
44C22×C4×D73—21no—
45C22×C4×D73—21no—
46C22×C4×D73—21no—
47C22×C4×D73—21no—
48C22×C4×D73C2×C412yes—
49C22×C4×D73Q812yes—
50C22×#10596831—21no—
51C22×#10596831—21no—
52C22×#10596831—21no—
53C22×#10596831—21no—
54C22×#10596831C2×C412yes—
55C22×#10596831D412yes—
56C22×#10596831D412yes—
57C2×C4⋊Dic73—21no—
58C2×C4⋊Dic73—21no—
59C2×C4⋊Dic73—21no—
60C2×C4⋊Dic73—21no—
61C2×C4⋊Dic73—21no—
62C2×C4⋊Dic73—21no—
63C2×C4⋊Dic73—21no—
64C2×C4⋊Dic73—21no—
65C2×C4⋊Dic73—21no—
66C2×C4⋊Dic73—21no—
67C2×C4⋊Dic73D412yes—
68C2×C4⋊Dic73D412yes—
69C2×#11924005—24no—
70C2×#11924005—24no—
71C2×#11924005—42no—
72C2×#11924005—42no—
73C2×#11924005—42no—
74C2×#11924005—42no—
75#14556522—28no—
76#14556503—28no—
77#14556498—24no—
78#14556498—24no—
79C23×C4×C73—21no—
80C23×C4×C73—21no—
81C23×C4×C73C2311yescharacteristic
82C22×C8×C73—21no—
83C22×C8×C73—21no—
84C22×C8×C73—21no—
85C22×C8×C73—21no—
86C22×C8×C73—21no—
87C22×C8×C73—21no—
88C22×C8×C73C2×C412yes—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73D412yes—
100C2×C4⋊C4×C73D412yes—
101C23×D73—21no—
102C23×D73—21no—
103C23×D73—21no—
104C23×D73—21no—
105C23×D73—21no—
106C23×D73—21no—
107C23×D73—21no—
108C23×D73—21no—
109C23×D73—21no—
110C23×D73—21no—
111C23×D73—21no—
112C23×D73—21no—
113C23×D73C4⋊C412yes—
114C23×D73SD1612yes—
115C23×D73SD1612yes—
116C22×Dic73—21no—
117C22×Dic73—21no—
118C22×Dic73—21no—
119C22×Dic73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—22no—
123C22×Dic73—22no—
124C22×Dic73—41no—
125C22×Dic73—41no—
126C22×Dic73—41no—
127C22×Dic73—41no—
128C22×Dic73—41no—
129C22×Dic73—41no—
130C22×Dic73—41no—
131C22×Dic73—41no—
132C22×Dic73—41no—
133C22×Dic73—41no—
134C22×Dic73—41no—
135C22×Dic73—41no—
136C22×Dic73C4⋊C412yes—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—22no—
149C2×C4×D73—41no—
150C2×C4×D73—41no—
151C2×C4×D73—41no—
152C2×C4×D73—41no—
153C2×C4×D73—41no—
154C2×C4×D73—41no—
155C2×C4×D73—41no—
156C2×C4×D73—41no—
157C2×C4×D73—41no—
158C2×C4×D73—41no—
159C2×C4×D73—41no—
160C2×C4×D73—41no—
161C2×C4×D73—41no—
162C2×C4×D73—41no—
163C2×C4×D73—41no—
164C2×C4×D73—41no—
165C2×#10596831—22no—
166C2×#10596831—22no—
167C2×#10596831—22no—
168C2×#10596831—22no—
169C2×#10596831—22no—
170C2×#10596831—22no—
171C2×#10596831C22⋊C414yescomplemented
172C4⋊Dic73—22no—
173C4⋊Dic73—22no—
174C4⋊Dic73—22no—
175C4⋊Dic73—22no—
176C4⋊Dic73—41no—
177C4⋊Dic73—41no—
178C4⋊Dic73—41no—
179C4⋊Dic73—41no—
180#11924005—48no—
181#11924005—48no—
182C24×C73C2×D411yescharacteristic
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—41no—
186C22×C4×C73—41no—
187C22×C4×C73—41no—
188C22×C4×C73—41no—
189C22×C4×C73—41no—
190C22×C4×C73—41no—
191C22×C4×C73—41no—
192C22×C4×C73—41no—
193C22×C4×C73—41no—
194C22×C4×C73—41no—
195C22×C4×C73—41no—
196C22×C4×C73—41no—
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×Q811yescharacteristic
205C22×C4×C73#4111yescharacteristic
206C22×C4×C73#4111yescharacteristic
207C22×C4×C73#4111yescharacteristic
208C22×C4×C73#4111yescharacteristic
209C22×C4×C73#4111yescharacteristic
210C22×C4×C73#4111yescharacteristic
211C2×C8×C73—22no—
212C2×C8×C73—22no—
213C2×C8×C73—22no—
214C2×C8×C73—41no—
215C2×C8×C73—41no—
216C2×C8×C73—41no—
217C2×C8×C73—41no—
218C4⋊C4×C73—22no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—41no—
223C4⋊C4×C73—41no—
224C4⋊C4×C73—41no—
225C4⋊C4×C73—41no—
226C23×C73C2×C4⋊C411yescharacteristic
227C23×C73#12011yescharacteristic
228C23×C73#12011yescharacteristic
229C23×C73#12111yescharacteristic
230C23×C73#12111yescharacteristic
231C23×C73#12311yescharacteristic
232C23×C73#12311yescharacteristic
233C23×C73C2×SD1611yescharacteristic
234C23×C73C2×SD1611yescharacteristic
235C23×C73#13511yescharacteristic
236C23×C73#13511yescharacteristic
237C23×C73AGL(1,ℤ/8)11yescharacteristic
238C23×C73AGL(1,ℤ/8)11yescharacteristic
239C23×C73#13711yescharacteristic
240C23×C73#13711yescharacteristic
241C22×D73—22no—
242C22×D73—22no—
243C22×D73—22no—
244C22×D73—22no—
245C22×D73—22no—
246C22×D73—22no—
247C22×D73—22no—
248C22×D73—22no—
249C22×D73—22no—
250C22×D73—22no—
251C22×D73—22no—
252C22×D73—22no—
253C22×D73—22no—
254C22×D73—22no—
255C22×D73—22no—
256C22×D73—22no—
257C22×D73—22no—
258C22×D73—22no—
259C22×D73—41no—
260C22×D73—41no—
261C22×D73—41no—
262C22×D73—41no—
263C22×D73—41no—
264C22×D73—41no—
265C22×D73—41no—
266C22×D73—41no—
267C22×D73—41no—
268C22×D73—41no—
269C22×D73—41no—
270C22×D73—41no—
271C22×D73—41no—
272C22×D73—41no—
273C22×D73—41no—
274C22×D73—41no—
275C22×D73#10614yescomplemented
276C2×C4×C73—42no—
277C2×C4×C73—42no—
278C2×C4×C73—42no—
279C2×C4×C73—42no—
280C2×C4×C73—42no—
281C2×C4×C73—42no—
282C2×C4×C73—81no—
283C2×C4×C73—81no—
284C2×C4×C73—81no—
285C2×C4×C73—81no—
286C2×C4×C73—81no—
287C2×C4×C73—81no—
288C2×C4×C73—81no—
289C2×C4×C73—81no—
290C2×C4×C73C2×C22⋊C411yescharacteristic
291C2×C4×C73#11711yescharacteristic
292C2×C4×C73C4×D411yescharacteristic
293C2×C4×C73C4×D411yescharacteristic
294C2×C4×C73C4×D411yescharacteristic
295C2×C4×C73C4×D411yescharacteristic
296C2×C4×C73#12011yescharacteristic
297C2×C4×C73#12111yescharacteristic
298C2×C4×C73#12111yescharacteristic
299C2×C4×C73#12111yescharacteristic
300C2×C4×C73#12111yescharacteristic
301C2×C4×C73#12111yescharacteristic
302C2×C4×C73#12111yescharacteristic
303C2×C4×C73C22⋊Q811yescharacteristic
304C2×C4×C73C22⋊Q811yescharacteristic
305C2×C4×C73C22⋊Q811yescharacteristic
306C2×C4×C73C22⋊Q811yescharacteristic
307C2×C4×C73C22⋊Q811yescharacteristic
308C2×C4×C73C22⋊Q811yescharacteristic
309C2×C4×C73#12311yescharacteristic
310C2×C4×C73#12311yescharacteristic
311C2×C4×C73#12311yescharacteristic
312C2×C4×C73#12411yescharacteristic
313C2×C4×C73#12411yescharacteristic
314C2×C4×C73#12411yescharacteristic
315C2×C4×C73#12611yescharacteristic
316C2×C4×C73#12611yescharacteristic
317C2×C4×C73#12711yescharacteristic
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—41no—
322C2×Dic73—41no—
323C2×Dic73—41no—
324C2×Dic73—41no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73—81no—
332C2×Dic73—81no—
333C2×Dic73—81no—
334C2×Dic73—81no—
335C2×Dic73—81no—
336C2×Dic73—81no—
337C2×Dic73—81no—
338C2×Dic73—81no—
339C4×D73—42no—
340C4×D73—42no—
341C4×D73—42no—
342C4×D73—42no—
343C4×D73—42no—
344C4×D73—42no—
345C4×D73—42no—
346C4×D73—42no—
347C8×C73—42no—
348#10596831—24no—
349C22×C73#38011yescharacteristic
350C22×C73#38511yescharacteristic
351C22×C73#38511yescharacteristic
352C22×C73#39211yescharacteristic
353C22×C73#39411yescharacteristic
354C22×C73#39411yescharacteristic
355C22×C73#39711yescharacteristic
356C22×C73C2×#10611yescharacteristic
357C22×C73#42711yescharacteristic
358C22×C73#42811yescharacteristic
359C22×C73#42811yescharacteristic
360C22×C73#44811yescharacteristic
361C22×C73#44811yescharacteristic
362C22×C73#44911yescharacteristic
363C22×C73#44911yescharacteristic
364C22×C73#45011yescharacteristic
365C22×C73#45011yescharacteristic
366C22×C73#45211yescharacteristic
367C22×C73#45211yescharacteristic
368C22×C73#46511yescharacteristic
369C22×C73#46511yescharacteristic
370C22×C73#46511yescharacteristic
371C22×C73#46511yescharacteristic
372C22×C73#46811yescharacteristic
373C22×C73#46811yescharacteristic
374C22×C73#46911yescharacteristic
375C22×C73#47011yescharacteristic
376C22×C73#48111yescharacteristic
377C22×C73#48111yescharacteristic
378C22×C73#48211yescharacteristic
379C22×C73#48211yescharacteristic
380C22×C73#48311yescharacteristic
381C22×C73#48311yescharacteristic
382C22×C73#48511yescharacteristic
383C22×C73#48511yescharacteristic
384C2×D73—24no—
385C2×D73—24no—
386C2×D73—24no—
387C2×D73—42no—
388C2×D73—42no—
389C2×D73—42no—
390C2×D73—42no—
391C2×D73—42no—
392C2×D73—42no—
393C2×D73—42no—
394C2×D73—42no—
395C2×D73—42no—
396C2×D73—42no—
397C2×D73—42no—
398C2×D73—42no—
399C4×C73—82no—
400C4×C73—82no—
401C4×C73#38611yescharacteristic
402C4×C73#38811yescharacteristic
403C4×C73#38811yescharacteristic
404C4×C73#39011yescharacteristic
405C4×C73#39311yescharacteristic
406C4×C73#39611yescharacteristic
407C4×C73#39611yescharacteristic
408C4×C73#39911yescharacteristic
409Dic73—42no—
410Dic73—82no—
411Dic73—82no—
412#11095—731nomaximal, Sylow
413C2×C73#143911yescharacteristic
414C2×C73#180711yescharacteristic
415C2×C73#180911yescharacteristic
416C2×C73#185311yescharacteristic
417C2×C73#185311yescharacteristic
418C2×C73#185411yescharacteristic
419C2×C73#185411yescharacteristic
420C2×C73#200011yescharacteristic
421C2×C73#200011yescharacteristic
422C2×C73#203411yescharacteristic
423C2×C73#203411yescharacteristic
424C2×C73#203511yescharacteristic
425C2×C73#203511yescharacteristic
426C2×C73#207711yescharacteristic
427C2×C73#207711yescharacteristic
428D73—44no—
429C22×#106—731no—
430C22×C22⋊C8—731no—
431C2×#380—731no—
432C2×#380—731no—
433C2×#340—731no—
434C2×#340—731no—
435C2×#340D7311yescharacteristic, complemented
436C73#1109511yescharacteristic, complemented, Sylow
437C24×C4—731no—
438C23×C8—731no—
439C23×C8C2×D7311yescharacteristic
440C22×C4⋊C4—731no—
441C22×C4⋊C4—731no—
442C22×C4⋊C4C2×D7311yescharacteristic
443C22×C4⋊C4C2×D7311yescharacteristic
444C22×C22⋊C4—1461no—
445C22×C22⋊C4—1461no—
446C2×#106—1462no—
447C2×#106—1462no—
448C2×#106—1462no—
449C2×C22⋊C8—734no—
450C2×C22⋊C8—1462no—
451C2×C22⋊C8—1462no—
452#380—1462no—
453#380—1462no—
454#380—1462no—
455#380—1462no—
456C2×#95—1461no—
457C2×#95—1461no—
458#340—22no—
459#340—1462no—
460#340—1462no—
461C25—731no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—731no—
465C23×C4—732no—
466C23×C4—732no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4—1461no—
470C23×C4—1461no—
471C23×C4—1461no—
472C23×C4—1461no—
473C23×C4—1461no—
474C23×C4—1461no—
475C23×C4—1461no—
476C23×C4—1461no—
477C23×C4—1461no—
478C23×C4—1461no—
479C23×C4—1461no—
480C23×C4—1461no—
481C23×C4C22×D7311yescharacteristic
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—732no—
489C22×C8—732no—
490C22×C8—732no—
491C22×C8—1461no—
492C22×C8—1461no—
493C22×C8—1461no—
494C22×C8—1461no—
495C22×C8C4×D7312yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—732no—
507C2×C4⋊C4—732no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4—1461no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4D29212yes—
519C2×C4⋊C4C22⋊D7312yes—
520C2×C22⋊C4—2922no—
521C2×C22⋊C4—2922no—
522C2×C22⋊C4—2922no—
523C2×C22⋊C4—2922no—
524C2×C22⋊C4—1464no—
525C2×C22⋊C4—1464no—
526#106—1468no—
527C22⋊C8—1468no—
528#95—1464no—
529#95—1464no—
530C24—732no—
531C24—732no—
532C24—732no—
533C24—1461no—
534C24—1461no—
535C24—1461no—
536C24—1461no—
537C24—1461no—
538C24—1461no—
539C24—1461no—
540C24—1461no—
541C24—1461no—
542C24—1461no—
543C24—1461no—
544C24—1461no—
545C24D4×D7311yescharacteristic
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—2921no—
561C22×C4—2921no—
562C22×C4—2921no—
563C22×C4—2921no—
564C22×C4—2921no—
565C22×C4—2921no—
566C22×C4—2921no—
567C22×C4—2921no—
568C22×C4—2921no—
569C22×C4—2921no—
570C22×C4—2921no—
571C22×C4—2921no—
572C22×C4—2921no—
573C22×C4—2921no—
574C22×C4—2921no—
575C22×C4—2921no—
576C22×C4—2921no—
577C22×C4—2921no—
578C22×C4—2921no—
579C22×C4—2921no—
580C22×C4—2921no—
581C22×C4—2921no—
582C22×C4—2921no—
583C22×C4—2921no—
584C22×C4—2921no—
585C22×C4—2921no—
586C22×C4—2921no—
587C22×C4—2921no—
588C22×C4—732no—
589C22×C4—1462no—
590C22×C4—1462no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4—1462no—
600C22×C4—1462no—
601C22×C4—1462no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4—1462no—
605C22×C4—1462no—
606C22×C4—1462no—
607C22×C4—1462no—
608C22×C4—1462no—
609C22×C4C2×C4×D7311yescharacteristic
610C22×C4D4×D7311yescharacteristic
611C22×C4D4×D7311yescharacteristic
612C22×C4D4×D7311yescharacteristic
613C22×C4D4×D7311yescharacteristic
614C22×C4C2×C22⋊D7311yescharacteristic
615C22×C4C2×D29211yescharacteristic
616C22×C4Q8×D7311yescharacteristic
617C22×C4#1192402711yescharacteristic
618C22×C4#1192402811yescharacteristic
619C22×C4#1192402811yescharacteristic
620C22×C4#1192402811yescharacteristic
621C22×C4#1192402811yescharacteristic
622C22×C4#1192402911yescharacteristic
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—734no—
631C2×C8—1462no—
632C2×C8—1462no—
633C2×C8—1462no—
634C2×C8—1462no—
635C2×C8—1462no—
636C2×C8—1462no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—2921no—
646C4⋊C4—2921no—
647C4⋊C4—2921no—
648C4⋊C4—2921no—
649C4⋊C4—1462no—
650C4⋊C4—1462no—
651C4⋊C4—1462no—
652C4⋊C4—1462no—
653C22⋊C4—2928no—
654C22⋊C4—2928no—
655C23—2921no—
656C23—2921no—
657C23—2921no—
658C23—2921no—
659C23—2921no—
660C23—2921no—
661C23—2921no—
662C23—2921no—
663C23—2921no—
664C23—2921no—
665C23—2921no—
666C23—2921no—
667C23—2921no—
668C23—2921no—
669C23—2921no—
670C23—2921no—
671C23—734no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1462no—
676C23—1462no—
677C23—1462no—
678C23—1462no—
679C23—1462no—
680C23—1462no—
681C23—1462no—
682C23—1462no—
683C23—1462no—
684C23—1462no—
685C23—1462no—
686C23—1462no—
687C23—1462no—
688C23—1462no—
689C23—1462no—
690C23C4⋊C4×D7311yescharacteristic
691C23#1455655911yescharacteristic
692C23#1455656111yescharacteristic
693C23#1455656411yescharacteristic
694C23#1455656411yescharacteristic
695C23#1455657311yescharacteristic
696C23#1455657611yescharacteristic
697C23SD16×D7311yescharacteristic
698C23SD16×D7311yescharacteristic
699C23#1455661011yescharacteristic
700C23#1455661411yescharacteristic
701C23#1455661511yescharacteristic
702C23#1455661811yescharacteristic
703C23#1455662011yescharacteristic
704C23#1455662311yescharacteristic
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—2921no—
720C2×C4—2921no—
721C2×C4—2921no—
722C2×C4—2921no—
723C2×C4—2922no—
724C2×C4—2922no—
725C2×C4—2922no—
726C2×C4—2922no—
727C2×C4—2922no—
728C2×C4—2922no—
729C2×C4—2922no—
730C2×C4—2922no—
731C2×C4—2922no—
732C2×C4—2922no—
733C2×C4—2922no—
734C2×C4—2922no—
735C2×C4—2922no—
736C2×C4—2922no—
737C2×C4—5841no—
738C2×C4—5841no—
739C2×C4—5841no—
740C2×C4—5841no—
741C2×C4—5841no—
742C2×C4—5841no—
743C2×C4—5841no—
744C2×C4—5841no—
745C2×C4—1462no—
746C2×C4—1462no—
747C2×C4—1462no—
748C2×C4C22⋊C4×D7311yescharacteristic
749C2×C4#1455654811yescharacteristic
750C2×C4#1455655111yescharacteristic
751C2×C4C4×C22⋊D7311yescharacteristic
752C2×C4#1455655311yescharacteristic
753C2×C4C4×D29211yescharacteristic
754C2×C4#1455656111yescharacteristic
755C2×C4#1455656311yescharacteristic
756C2×C4#1455656411yescharacteristic
757C2×C4#1455656411yescharacteristic
758C2×C4#1455656411yescharacteristic
759C2×C4#1455656511yescharacteristic
760C2×C4#1455656611yescharacteristic
761C2×C4#1455656711yescharacteristic
762C2×C4#1455656911yescharacteristic
763C2×C4#1455656911yescharacteristic
764C2×C4#1455656911yescharacteristic
765C2×C4#1455656911yescharacteristic
766C2×C4#1455657111yescharacteristic
767C2×C4#1455657411yescharacteristic
768C2×C4#1455657611yescharacteristic
769C2×C4#1455657611yescharacteristic
770C2×C4#1455657711yescharacteristic
771C2×C4#1455657711yescharacteristic
772C2×C4#1455657911yescharacteristic
773C2×C4#1455658511yescharacteristic
774C2×C4#1455658611yescharacteristic
775C2×C4#1455658711yescharacteristic
776C8—42no—
777C8—1464no—
778C22—2922no—
779C22—2922no—
780C22—2922no—
781C22—2922no—
782C22—2922no—
783C22—2922no—
784C22—2922no—
785C22—2922no—
786C22—2922no—
787C22—2922no—
788C22—2922no—
789C22—2922no—
790C22—1464no—
791C22—1464no—
792C22—1464no—
793C22#1798844611yescharacteristic
794C22#1798845811yescharacteristic
795C22#1798846111yescharacteristic
796C22#1798849611yescharacteristic
797C22#1798850211yescharacteristic
798C22#1798850511yescharacteristic
799C22#1798851611yescharacteristic
800C22#106×D7311yescharacteristic
801C22#1798862411yescharacteristic
802C22#1798862611yescharacteristic
803C22#1798862811yescharacteristic
804C22#1798872411yescharacteristic
805C22#1798872711yescharacteristic
806C22#1798872911yescharacteristic
807C22#1798873511yescharacteristic
808C22#1798873611yescharacteristic
809C22#1798873911yescharacteristic
810C22#1798874811yescharacteristic
811C22#1798875011yescharacteristic
812C22#1798881511yescharacteristic
813C22#1798881511yescharacteristic
814C22#1798881911yescharacteristic
815C22#1798881911yescharacteristic
816C22#1798883211yescharacteristic
817C22#1798883611yescharacteristic
818C22#1798883911yescharacteristic
819C22#1798884411yescharacteristic
820C22#1798890411yescharacteristic
821C22#1798890711yescharacteristic
822C22#1798890911yescharacteristic
823C22#1798891411yescharacteristic
824C22#1798891611yescharacteristic
825C22#1798891911yescharacteristic
826C22#1798892711yescharacteristic
827C22#1798893011yescharacteristic
828C4—82no—
829C4—82no—
830C4—2922no—
831C4—5842no—
832C4—5842no—
833C4#1798846511yescharacteristic
834C4#1798847611yescharacteristic
835C4#1798847811yescharacteristic
836C4#1798848711yescharacteristic
837C4#1798850011yescharacteristic
838C4#1798850911yescharacteristic
839C4#1798851111yescharacteristic
840C4#1798852211yescharacteristic
841C2—2924no—
842C2#2260817511yescharacteristic
843C2#2260995511yescharacteristic
844C2#2260996311yescharacteristic
845C2#2261012211yescharacteristic
846C2#2261012511yescharacteristic
847C2#2261012711yescharacteristic
848C2#2261013311yescharacteristic
849C2#2261093311yescharacteristic
850C2#2261093511yescharacteristic
851C2#2261111811yescharacteristic
852C2#2261112311yescharacteristic
853C2#2261112511yescharacteristic
854C2#2261113011yescharacteristic
855C2#2261136911yescharacteristic
856C2#2261137011yescharacteristic
subgroupG/H
centerC24D4×D73
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC2×#340×C73C2
socleC24×C73C2×D4
prime radicalC24×D73D4
cosocleC23×C4×C73C23
hypercenterC2×#340D73
hypocenterC73#11095
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#14556522C2semidirect
5. C2×#17988350C2semidirect
6. C2×#17988349C2semidirect
7. C2×#340×C73C2semidirect
19. C2×#14556503C4semidirect
171. C2×#10596831C22⋊C4semidirect
275. C22×D73#106semidirect
435. C2×#340D73semidirect
436. C73#11095semidirect

Maximal subgroups

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

subgroupindex
C22×#145565222
C22×#145565032
C2×#179884442
C2×#179883502
C2×#179883492
C2×#340×C732
#1109573