Finite Group Databasebeta

← C2×#22621792 #33962363

Subgroups — C2×#22621792 #33962363

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D73C211yesmaximal, characteristic, complemented
2C2×#17989238C211yesmaximal, characteristic
3#22621792C2116yesmaximal, direct product factor
4C2×#17988936C211yesmaximal, characteristic, complemented
5C2×#17988917C211yesmaximal, characteristic, complemented
6C2×#17988916C211yesmaximal, characteristic, complemented
7C2×#17988870C211yesmaximal, characteristic, complemented
8C2×#17988819C211yesmaximal, characteristic, complemented
9C2×#17988816C211yesmaximal, characteristic, complemented
10C2×#17988791C211yesmaximal, characteristic, complemented
11C2×#17988727C211yesmaximal, characteristic, complemented
12C2×#17988726C211yesmaximal, characteristic, complemented
13C2×#17988672C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D73C211yesmaximal, characteristic, complemented
15C2×#103×D73C211yesmaximal, characteristic, complemented
16C22×#103×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×Q8×D73C2211yescharacteristic
19C22×#11924017C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×C8×D73C2211yescharacteristic
23Q8×C22⋊D73—24no—
24Q8×C22⋊D73C2218yescomplemented
25#17989238—24no—
26#17989238C2218yes—
27C2×#14556590C2211yescharacteristic
28C2×#14556589—21no—
29C2×#14556589C2211yescharacteristic
30C2×#14556576—21no—
31C2×#14556574—21no—
32C2×#14556570—21no—
33C2×#14556570C2211yescharacteristic
34C2×#14556569—21no—
35C2×#14556567—21no—
36C2×#14556567C2211yescharacteristic
37C2×#14556566C2211yescharacteristic
38C2×#14556565C2211yescharacteristic
39C2×Q8×Dic73C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C2×C4×C22⋊D73—21no—
42C2×C4×C22⋊D73C2211yescharacteristic
43C2×C4⋊C4×D73C2211yescharacteristic
44#17988936C2218yescomplemented
45#17988917C2218yescomplemented
46#17988916C2218yescomplemented
47#17988870C2218yescomplemented
48#17988819C2218yescomplemented
49#17988816C2218yescomplemented
50#17988791C2218yescomplemented
51#17988727C2218yescomplemented
52#17988726C2218yescomplemented
53#17988672C2218yescomplemented
54C8×C22⋊D73C2218yescomplemented
55C2×#14556523C2211yescharacteristic
56C2×#14556522C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64#103×D73C2218yescomplemented
65C2×#14556513C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C23×Q8×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72C2×#103×C73C2211yescharacteristic
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2218yescomplemented
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146C2311yescharacteristic
82C2×Q8×D73—22no—
83C2×Q8×D73—24no—
84C2×Q8×D73—42no—
85C2×Q8×D73C2314yes—
86C22×D292—21no—
87C22×D292C2311yescharacteristic
88C22×C22⋊D73—21no—
89C22×C22⋊D73D411yescharacteristic
90C22×C4×D73—21no—
91C22×C4×D73—21no—
92C22×C4×D73—21no—
93C22×C4×D73C2311yescharacteristic
94C2×#11924017—42no—
95C2×#11924017C2314yes—
96C2×#11924015—24no—
97C2×#11924015—42no—
98C2×#11924015C2314yes—
99C2×#11924015C2314yes—
100C22×#10596831C2311yescharacteristic
101C22×#10596831C2311yescharacteristic
102C2×C8×D73—42no—
103C2×C8×D73C2314yes—
104#14556590—22no—
105#14556590C2314yes—
106#14556589—28no—
107#14556589—22no—
108#14556589C2314yes—
109#14556576—28no—
110#14556574—28no—
111#14556570—28no—
112#14556570—22no—
113#14556570C2314yes—
114#14556569—28no—
115#14556567—22no—
116#14556567—28no—
117#14556567C2314yes—
118#14556566—22no—
119#14556566C2314yes—
120#14556565—22no—
121#14556565C2314yes—
122Q8×Dic73—22no—
123Q8×Dic73C2314yes—
124#14556553—22no—
125#14556553C2314yes—
126C4×C22⋊D73—28no—
127C4×C22⋊D73D414yes—
128C4×C22⋊D73C2314yes—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007D411yescharacteristic
139C4⋊C4×D73—22no—
140C4⋊C4×D73C2314yes—
141C2×C22⋊Dic73—21no—
142C2×C22⋊Dic73D411yescharacteristic
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005D411yescharacteristic
148C2×C4×Dic73—21no—
149C2×C4×Dic73C2311yescharacteristic
150#14556523C2314yes—
151#14556522C2314yes—
152#14556522C2314yes—
153#14556520C2314yes—
154#14556516C2314yes—
155#14556515C2314yes—
156#14556515C2314yes—
157#14556514C2314yes—
158#14556514C2314yes—
159#14556513C2314yes—
160C22⋊#10596831C2314yes—
161#14556503C2314yes—
162C8×Dic73C2314yes—
163C22×Q8×C73—21no—
164C22×Q8×C73—22no—
165C22×Q8×C73—24no—
166C22×Q8×C73—42no—
167C22×Q8×C73C2311yescharacteristic
168C22×Q8×C73C2314yes—
169C22×Q8×C73C2311yescharacteristic
170C23×C4×C73—21no—
171C23×C4×C73—21no—
172C23×C4×C73C2311yescharacteristic
173C22×C8×C73—42no—
174C22×C8×C73C2311yescharacteristic
175C22×C8×C73C2311yescharacteristic
176C22×C8×C73C2314yes—
177C2×C4⋊C4×C73—22no—
178C2×C4⋊C4×C73—21no—
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C4⋊C4×C73C2311yescharacteristic
181C2×C4⋊C4×C73C2314yes—
182#103×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185#103×C73C2314yes—
186C23×D73—21no—
187C23×D73C2×D411yescharacteristic
188#11924028—432no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—21no—
192C2×Dic146—24no—
193C2×Dic146—24no—
194C2×Dic146—44no—
195C2×Dic146—44no—
196C2×Dic146C2412yes—
197Q8×D73—28no—
198Q8×D73—44no—
199Q8×D73—48no—
200C2×D292—22no—
201C2×D292—22no—
202C2×D292—24no—
203C2×D292—21no—
204C2×D292—44no—
205C2×D292C2412yes—
206C2×C22⋊D73—24no—
207C2×C22⋊D73—44no—
208C2×C22⋊D73SD1618yescomplemented
209C2×C22⋊D73C2×D414yes—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73C2×D411yescharacteristic
214C22×Dic73C2×D411yescharacteristic
215C22×Dic73C2×D411yescharacteristic
216C2×C4×D73—22no—
217C2×C4×D73—22no—
218C2×C4×D73—24no—
219C2×C4×D73—24no—
220C2×C4×D73—24no—
221C2×C4×D73—44no—
222C2×C4×D73—44no—
223C2×C4×D73—44no—
224C2×C4×D73C2×D412yes—
225C2×C4×D73C2412yes—
226#11924017—44no—
227#11924015—28no—
228#11924015—44no—
229C2×#10596831—22no—
230C2×#10596831—22no—
231C2×#10596831C2412yes—
232C2×#10596831C2412yes—
233C8×D73—44no—
234C4⋊Dic73—21no—
235C4⋊Dic73—21no—
236C4⋊Dic73—24no—
237C4⋊Dic73C2412yes—
238C4⋊Dic73C2412yes—
239#11924007—24no—
240#11924007—24no—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924007C2×D414yes—
246C22⋊Dic73—24no—
247C22⋊Dic73C2×D414yes—
248#11924005—24no—
249#11924005—24no—
250#11924005—24no—
251#11924005—24no—
252#11924005C2×D414yes—
253C4×Dic73—24no—
254C4×Dic73C2×D412yes—
255C4×Dic73C2412yes—
256C24×C73C2×D411yescharacteristic
257C2×Q8×C73—21no—
258C2×Q8×C73—24no—
259C2×Q8×C73—21no—
260C2×Q8×C73—22no—
261C2×Q8×C73—28no—
262C2×Q8×C73—22no—
263C2×Q8×C73—22no—
264C2×Q8×C73—44no—
265C2×Q8×C73—44no—
266C2×Q8×C73—48no—
267C2×Q8×C73#4114yescomplemented
268C2×Q8×C73C2412yes—
269C2×Q8×C73C2412yes—
270C22×C4×C73—21no—
271C22×C4×C73—22no—
272C22×C4×C73—22no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—24no—
276C22×C4×C73—21no—
277C22×C4×C73—24no—
278C22×C4×C73—44no—
279C22×C4×C73—44no—
280C22×C4×C73C2×D411yescharacteristic
281C22×C4×C73C2×D412yes—
282C22×C4×C73C2412yes—
283C22×C4×C73C2411yescharacteristic
284C2×C8×C73—22no—
285C2×C8×C73—22no—
286C2×C8×C73—44no—
287C2×C8×C73C2412yes—
288C2×C8×C73C2412yes—
289C4⋊C4×C73—21no—
290C4⋊C4×C73—21no—
291C4⋊C4×C73—24no—
292C4⋊C4×C73C2412yes—
293C4⋊C4×C73C2412yes—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73C2×SD1614yes—
297C23×C73C22×D412yes—
298C23×C73C22×D411yescharacteristic
299C22×D73—22no—
300C22×D73—22no—
301C22×D73—22no—
302C22×D73—42no—
303C22×D73—42no—
304C22×D73—42no—
305C22×D73C2×SD1614yes—
306C22×D73C22×D412yes—
307Q8×C73—24no—
308Q8×C73—22no—
309Q8×C73—22no—
310Q8×C73—22no—
311Q8×C73—48no—
312Q8×C73—42no—
313Q8×C73C2×#4114yescomplemented
314C2×C4×C73—22no—
315C2×C4×C73—24no—
316C2×C4×C73—22no—
317C2×C4×C73—24no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—48no—
324C2×C4×C73—42no—
325C2×C4×C73—42no—
326C2×C4×C73—42no—
327C2×C4×C73—48no—
328C2×C4×C73C22×D412yes—
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C2×#4112yes—
331C2×C4×C73H(5,𝔽2)12yes—
332C2×C4×C73C2511yescharacteristic
333C22⋊D73—48no—
334C22⋊D73C2×SD16116yescomplemented
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—42no—
341C2×Dic73—42no—
342C2×Dic73—42no—
343C2×Dic73C2×SD1614yes—
344C2×Dic73C22×D412yes—
345C2×Dic73C22×D412yes—
346C2×Dic73C22×D412yes—
347D292—22no—
348D292—22no—
349D292—48no—
350D292—42no—
351C4×D73—24no—
352C4×D73—22no—
353C4×D73—22no—
354C4×D73—48no—
355C4×D73—48no—
356C4×D73—48no—
357Dic146—22no—
358Dic146—22no—
359Dic146—48no—
360Dic146—42no—
361Dic146—48no—
362C8×C73—22no—
363C8×C73—22no—
364#10596831—22no—
365#10596831—22no—
366C22×C73—22no—
367C22×C73—28no—
368C22×C73—22no—
369C22×C73#54612yes—
370C22×C73C22×SD1614yes—
371C22×C73C22×SD1612yes—
372C22×C73#57812yes—
373C22×C73C23×D411yescharacteristic
374C2×D73—22no—
375C2×D73—28no—
376C2×D73—22no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—84no—
381C2×D73C22×SD1614yes—
382C4×C73—24no—
383C4×C73—22no—
384C4×C73—42no—
385C4×C73—42no—
386C4×C73—42no—
387C4×C73#54612yes—
388C4×C73C22×#4111yescharacteristic
389C4×C73C2×H(5,𝔽2)11yescharacteristic
390Dic73—22no—
391Dic73—22no—
392Dic73—42no—
393Dic73—42no—
394Dic73—42no—
395Dic73C22×SD1614yes—
396C2×#3298—731nomaximal, Sylow
397C2×C73—24no—
398C2×C73#329814yescomplemented
399C2×C73C2×#54611yescharacteristic
400C2×C73C23×SD1611yescharacteristic
401C2×C73C2×#57811yescharacteristic
402D73—24no—
403D73—82no—
404C2×D4×Q8—731no—
405C2×#547—731no—
406#3298—7316no—
407C2×#487—731no—
408C2×#483—731no—
409C2×#483—731no—
410C2×#475—731no—
411C2×#465—731no—
412C2×#465—731no—
413C2×#461—731no—
414C2×#448—731no—
415C2×#448—731no—
416C2×C4×SD16—731no—
417C2×C8×D4—731no—
418C22×#103—731no—
419C22×#103D7311yescharacteristic, complemented
420C73C2×#329811yescharacteristic, complemented, Sylow
421C22×#41—1461no—
422C23×Q8—731no—
423C23×Q8C2×D7311yescharacteristic
424C22×SD16—731no—
425C22×SD16—731no—
426C22×SD16—731no—
427C23×C8—731no—
428C23×C8C2×D7311yescharacteristic
429D4×Q8—738no—
430D4×Q8—1464no—
431#547—738no—
432#547—1464no—
433C2×C4⋊Q8—731no—
434C2×C4⋊Q8—731no—
435C2×C4⋊Q8—1461no—
436C2×#123—1461no—
437C2×#123—1461no—
438C2×C22⋊Q8—731no—
439C2×C22⋊Q8—731no—
440C2×C22⋊Q8—1461no—
441C2×C22⋊Q8—1461no—
442C2×C22⋊Q8—1461no—
443C2×#121—731no—
444C2×#121—731no—
445C2×C4×Q8—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4—1461no—
449C22×C4⋊C4—731no—
450C22×C4⋊C4C2×D7311yescharacteristic
451#487—738no—
452#483—738no—
453#483—738no—
454#475—738no—
455#465—738no—
456#465—738no—
457#461—738no—
458#448—738no—
459#448—738no—
460C4×SD16—738no—
461C8×D4—738no—
462C2×#106—731no—
463C2×#106—731no—
464C2×#106—731no—
465C2×C4⋊C8—731no—
466C2×#103—731no—
467C2×#103—731no—
468C2×#103—731no—
469C2×#103—731no—
470C2×#103—731no—
471C2×#103—738no—
472C2×#103C2×D7311yescharacteristic
473C2×#103C2×D7311yescharacteristic
474C2×#103C2×D7311yescharacteristic
475C2×#103C2×D7311yescharacteristic
476C2×#103C2×D7318yescomplemented
477C2×#102—731no—
478C2×C22⋊C8—731no—
479C2×C22⋊C8—731no—
480C2×C4×C8—731no—
481C2×#41—2928no—
482C2×#41—1468no—
483C22×Q8—21no—
484C22×Q8—22no—
485C22×Q8—24no—
486C22×Q8—42no—
487C22×Q8—2922no—
488C22×Q8—734no—
489C22×Q8—731no—
490C22×Q8—1461no—
491C22×Q8—1461no—
492C22×Q8—1464no—
493C22×Q8—1462no—
494C22×Q8C22×D7311yescharacteristic
495C22×Q8C22×D7314yes—
496C22×Q8C22×D7311yescharacteristic
497C22×D4—731no—
498C22×D4—731no—
499C22×D4—1461no—
500C22×D4—1461no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—731no—
504C23×C4—1461no—
505C23×C4—1461no—
506C23×C4—1461no—
507C23×C4C22×D7311yescharacteristic
508C2×SD16—2922no—
509C2×SD16—2922no—
510C2×SD16—734no—
511C2×SD16—734no—
512C2×SD16—734no—
513C2×SD16—1464no—
514C22×C8—42no—
515C22×C8—2922no—
516C22×C8—734no—
517C22×C8—731no—
518C22×C8—731no—
519C22×C8C22×D7311yescharacteristic
520C22×C8C22×D7311yescharacteristic
521C22×C8C22×D7314yes—
522C4⋊Q8—734no—
523C4⋊Q8—734no—
524C4⋊Q8—1462no—
525C4⋊Q8—1462no—
526C4⋊Q8—1468no—
527#123—1468no—
528#123—1468no—
529C22⋊Q8—734no—
530C22⋊Q8—734no—
531C22⋊Q8—1468no—
532C22⋊Q8—1468no—
533C22⋊Q8—1468no—
534C22⋊Q8—1462no—
535C22⋊Q8—1462no—
536#121—734no—
537#121—734no—
538#121—1462no—
539#121—1462no—
540C4×Q8—734no—
541C4×Q8—1462no—
542C4×D4—734no—
543C4×D4—734no—
544C4×D4—734no—
545C4×D4—1462no—
546C4×D4—1468no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—731no—
550C2×C4⋊C4—731no—
551C2×C4⋊C4—731no—
552C2×C4⋊C4—734no—
553C2×C4⋊C4—1462no—
554C2×C4⋊C4—1461no—
555C2×C4⋊C4—1461no—
556C2×C4⋊C4—1461no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4—1461no—
559C2×C4⋊C4—1461no—
560C2×C4⋊C4—1461no—
561C2×C4⋊C4C22×D7311yescharacteristic
562C2×C4⋊C4C22×D7311yescharacteristic
563C2×C4⋊C4C22×D7314yes—
564C2×C22⋊C4—731no—
565C2×C22⋊C4—731no—
566C2×C22⋊C4—1461no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4—1461no—
569C2×C22⋊C4—1461no—
570C2×C22⋊C4—1461no—
571C2×C42—731no—
572C2×C42—1461no—
573#106—734no—
574#106—734no—
575#106—734no—
576C4⋊C8—734no—
577#103—734no—
578#103—734no—
579#103—734no—
580#103—734no—
581#103—734no—
582#103C22×D7314yes—
583#103C22×D7314yes—
584#103C22×D7314yes—
585#103C22×D7314yes—
586#102—734no—
587C22⋊C8—734no—
588C22⋊C8—734no—
589C4×C8—734no—
590C24—731no—
591C24—1461no—
592C24D4×D7311yescharacteristic
593#41—29232no—
594C2×Q8—21no—
595C2×Q8—24no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—28no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—48no—
604C2×Q8—2924no—
605C2×Q8—2924no—
606C2×Q8—2928no—
607C2×Q8—2924no—
608C2×Q8—732no—
609C2×Q8—1464no—
610C2×Q8—1464no—
611C2×Q8—1468no—
612C2×Q8—1462no—
613C2×Q8—1462no—
614C2×Q8—1461no—
615C2×Q8#1192402814yescomplemented
616C2×Q8C23×D7312yes—
617C2×Q8C23×D7312yes—
618C2×D4—2924no—
619C2×D4—2924no—
620C2×D4—738no—
621C2×D4—734no—
622C2×D4—732no—
623C2×D4—1464no—
624C2×D4—1464no—
625C2×D4—1461no—
626C2×D4—1462no—
627C2×D4—1462no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—2924no—
639C22×C4—2924no—
640C22×C4—2924no—
641C22×C4—731no—
642C22×C4—731no—
643C22×C4—731no—
644C22×C4—732no—
645C22×C4—732no—
646C22×C4—1464no—
647C22×C4—1464no—
648C22×C4—1464no—
649C22×C4—1461no—
650C22×C4—1461no—
651C22×C4—1461no—
652C22×C4—1462no—
653C22×C4—1462no—
654C22×C4D4×D7312yes—
655C22×C4D4×D7311yescharacteristic
656C22×C4C23×D7312yes—
657C22×C4C23×D7311yescharacteristic
658SD16—2924no—
659SD16—2924no—
660SD16—1468no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—2924no—
665C2×C8—732no—
666C2×C8—732no—
667C2×C8—1462no—
668C2×C8—1462no—
669C2×C8C23×D7312yes—
670C2×C8C23×D7312yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—734no—
675C4⋊C4—732no—
676C4⋊C4—732no—
677C4⋊C4—1464no—
678C4⋊C4—1464no—
679C4⋊C4—1464no—
680C4⋊C4—1464no—
681C4⋊C4—1464no—
682C4⋊C4—1464no—
683C4⋊C4—1464no—
684C4⋊C4—1461no—
685C4⋊C4—1461no—
686C4⋊C4C23×D7312yes—
687C4⋊C4C23×D7312yes—
688C22⋊C4—734no—
689C22⋊C4—734no—
690C22⋊C4—1464no—
691C22⋊C4—1464no—
692C22⋊C4—1464no—
693C22⋊C4—1464no—
694C22⋊C4—1464no—
695C42—732no—
696C42—732no—
697C42—1464no—
698C23—22no—
699C23—22no—
700C23—2922no—
701C23—2922no—
702C23—2922no—
703C23—732no—
704C23—734no—
705C23—1462no—
706C23—1462no—
707C23—1462no—
708C23SD16×D7314yes—
709C23C2×D4×D7312yes—
710C23C2×D4×D7311yescharacteristic
711Q8—22no—
712Q8—24no—
713Q8—22no—
714Q8—22no—
715Q8—48no—
716Q8—42no—
717Q8—2928no—
718Q8—2928no—
719Q8—2922no—
720Q8—1462no—
721Q8—1462no—
722Q8C2×#1192402814yescomplemented
723D4—2928no—
724D4—2928no—
725D4—2922no—
726D4—7316no—
727D4—1462no—
728D4—1462no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—48no—
743C2×C4—2928no—
744C2×C4—2928no—
745C2×C4—2928no—
746C2×C4—2922no—
747C2×C4—2922no—
748C2×C4—2922no—
749C2×C4—732no—
750C2×C4—734no—
751C2×C4—732no—
752C2×C4—732no—
753C2×C4—1462no—
754C2×C4—1462no—
755C2×C4—1462no—
756C2×C4—1462no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1462no—
760C2×C4—1464no—
761C2×C4C2×D4×D7312yes—
762C2×C4C2×D4×D7311yescharacteristic
763C2×C4C2×#1192402812yes—
764C2×C4#1455663612yes—
765C2×C4C24×D7311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1462no—
769C8—1462no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—2922no—
774C22—2922no—
775C22—2922no—
776C22—5844no—
777C22—734no—
778C22—1468no—
779C22—1462no—
780C22—1462no—
781C22#1798922712yes—
782C22C2×SD16×D7314yes—
783C22C2×SD16×D7312yes—
784C22#1798940012yes—
785C22C22×D4×D7311yescharacteristic
786C4—22no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—2922no—
792C4—2922no—
793C4—2922no—
794C4—734no—
795C4—1462no—
796C4—1462no—
797C4#1798922712yes—
798C4C22×#1192402811yescharacteristic
799C4C2×#1455663611yescharacteristic
800C2—24no—
801C2—5842no—
802C2—1464no—
803C2#2262179214yesdirect product factor
804C2C2×#1798922711yescharacteristic
805C2C22×SD16×D7311yescharacteristic
806C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC22×#103×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989238C2
hypercenterC22×#103D73
hypocenterC73C2×#3298
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D73C2semidirect
3. #22621792C2direct (N × H)
4. C2×#17988936C2semidirect
5. C2×#17988917C2semidirect
6. C2×#17988916C2semidirect
7. C2×#17988870C2semidirect
8. C2×#17988819C2semidirect
9. C2×#17988816C2semidirect
10. C2×#17988791C2semidirect
11. C2×#17988727C2semidirect
12. C2×#17988726C2semidirect
13. C2×#17988672C2semidirect
14. C2×C8×C22⋊D73C2semidirect
15. C2×#103×D73C2semidirect
16. C22×#103×C73C2semidirect
24. Q8×C22⋊D73C22semidirect
44. #17988936C22semidirect
45. #17988917C22semidirect
46. #17988916C22semidirect
47. #17988870C22semidirect
48. #17988819C22semidirect
49. #17988816C22semidirect
50. #17988791C22semidirect
51. #17988727C22semidirect
52. #17988726C22semidirect
53. #17988672C22semidirect
54. C8×C22⋊D73C22semidirect
64. #103×D73C22semidirect
76. C2×#103×C73C22semidirect
208. C2×C22⋊D73SD16semidirect
267. C2×Q8×C73#41semidirect
313. Q8×C73C2×#41semidirect
334. C22⋊D73C2×SD16semidirect
398. C2×C73#3298semidirect
419. C22×#103D73semidirect
420. C73C2×#3298semidirect
476. C2×#103C2×D73semidirect
615. C2×Q8#11924028semidirect
722. Q8C2×#11924028semidirect
803. C2#22621792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D732
C2×#179892382
#226217922
C2×#179889362
C2×#179889172
C2×#179889162
C2×#179888702
C2×#179888192
C2×#179888162
C2×#179887912
C2×#179887272
C2×#179887262
C2×#179886722
C2×C8×C22⋊D732
C2×#103×D732
C22×#103×C732
C2×#329873