Finite Group Databasebeta

← C2×#22621924 #33962560

Subgroups — C2×#22621924 #33962560

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989246C211yesmaximal, characteristic, complemented
2C2×#17989241C211yesmaximal, characteristic, complemented
3#22621924C2116yesmaximal, direct product factor
4C2×#17988947C211yesmaximal, characteristic, complemented
5C2×#17988923C211yesmaximal, characteristic, complemented
6C2×#17988901C211yesmaximal, characteristic, complemented
7C2×#17988883C211yesmaximal, characteristic, complemented
8C2×#17988833C211yesmaximal, characteristic, complemented
9C2×#17988823C211yesmaximal, characteristic, complemented
10C2×#17988803C211yesmaximal, characteristic, complemented
11C2×#17988734C211yesmaximal, characteristic, complemented
12C2×#17988728C211yesmaximal, characteristic, complemented
13C2×#17988689C211yesmaximal, characteristic, complemented
14C2×#17988589C211yesmaximal, characteristic, complemented
15C22×#14556516C211yesmaximal, characteristic, complemented
16C2×#435×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C22×#11924027—21no—
19C23×Dic146C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×D584C2211yescharacteristic
23#17989246—24no—
24#17989246C2218yescomplemented
25#17989241—24no—
26#17989241C2218yescomplemented
27C2×#14556591C2211yescharacteristic
28C2×#14556579C2211yescharacteristic
29C2×#14556577—21no—
30C2×#14556575—21no—
31C2×#14556575—21no—
32C2×#14556571—21no—
33C2×#14556570C2211yescharacteristic
34C2×#14556569—21no—
35C2×#14556565C2211yescharacteristic
36C2×#14556565C2211yescharacteristic
37C2×#14556565C2211yescharacteristic
38C2×#14556563—21no—
39C2×C4×Dic146C2211yescharacteristic
40C2×C4×D292C2211yescharacteristic
41C2×#14556551—21no—
42C22×C4⋊Dic73C2211yescharacteristic
43C22×C4⋊Dic73C2211yescharacteristic
44#17988947C2218yescomplemented
45#17988923C2218yescomplemented
46#17988901C2218yescomplemented
47#17988883C2218yescomplemented
48#17988833C2218yescomplemented
49#17988823C2218yescomplemented
50#17988803C2218yescomplemented
51#17988734C2218yescomplemented
52#17988728C2218yescomplemented
53#17988689C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556525C2211yescharacteristic
56C2×#14556525C2211yescharacteristic
57#17988589C2218yescomplemented
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2218yescomplemented
65C2×#14556513C2211yescharacteristic
66C2×#14556513C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C22×M16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#435×C73C2218yescomplemented
73C2×C4⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×C22⋊C8×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—22no—
79C2×#11924028—42no—
80C2×#11924028C2314yes—
81C2×#11924027—28no—
82C2×#11924027—48no—
83C22×Dic146—24no—
84C22×Dic146—21no—
85C22×Dic146—22no—
86C22×Dic146—21no—
87C22×Dic146—42no—
88C22×Dic146C2311yescharacteristic
89C22×Dic146C2314yes—
90C22×Dic146C2311yescharacteristic
91C22×D292C2311yescharacteristic
92C22×D292C2311yescharacteristic
93C22×C22⋊D73—21no—
94C22×C22⋊D73—21no—
95C22×C22⋊D73—21no—
96C22×C22⋊D73—21no—
97C23×Dic73—21no—
98C23×Dic73—21no—
99C23×Dic73—21no—
100C22×C4×D73—21no—
101C22×C4×D73—21no—
102C2×#11924017—24no—
103C2×#11924017—42no—
104C2×#11924017C2314yes—
105C2×#11924017C2314yes—
106C2×D584—42no—
107C2×D584C2314yes—
108#14556591—22no—
109#14556591C2314yes—
110#14556579—22no—
111#14556579C2314yes—
112#14556577—28no—
113#14556575—28no—
114#14556575—28no—
115#14556571—28no—
116#14556570—22no—
117#14556570C2314yes—
118#14556569—28no—
119#14556565—22no—
120#14556565—22no—
121#14556565—22no—
122#14556565C2314yes—
123#14556565C2314yes—
124#14556565C2314yes—
125#14556563—28no—
126C4×Dic146—22no—
127C4×Dic146C2314yes—
128C4×D292—22no—
129C4×D292C2314yes—
130#14556551—28no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73—22no—
133C2×C4⋊Dic73—22no—
134C2×C4⋊Dic73—21no—
135C2×C4⋊Dic73—21no—
136C2×C4⋊Dic73C2311yescharacteristic
137C2×C4⋊Dic73C2311yescharacteristic
138C2×C4⋊Dic73C2311yescharacteristic
139C2×C4⋊Dic73C2311yescharacteristic
140C2×C4⋊Dic73C2314yes—
141C2×C4⋊Dic73C2314yes—
142C2×#11924007—21no—
143C2×#11924007—21no—
144C2×C22⋊Dic73—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005—21no—
150C2×#11924005—21no—
151C2×C4×Dic73—21no—
152#14556525C2314yes—
153#14556525C2314yes—
154#14556525C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556516C2314yes—
158#14556516C2314yes—
159#14556516C2314yes—
160#14556516C2314yes—
161#14556513C2314yes—
162#14556513C2314yes—
163#14556513C2314yes—
164#14556513C2314yes—
165C22×D4×C73D411yescharacteristic
166C23×C4×C73C2311yescharacteristic
167C23×C4×C73C2311yescharacteristic
168C2×M16×C73—42no—
169C2×M16×C73C2314yes—
170C22×C8×C73—42no—
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175C22×C8×C73C2314yes—
176C4×D4×C73D414yes—
177C4×D4×C73C2314yes—
178C2×C4⋊C4×C73D411yescharacteristic
179C2×C22⋊C4×C73D411yescharacteristic
180C2×C22⋊C4×C73D411yescharacteristic
181C2×C42×C73C2311yescharacteristic
182C4⋊C8×C73C2314yes—
183C22⋊C8×C73C2314yes—
184C22⋊C8×C73C2314yes—
185#97×C73C2314yes—
186C23×D73—21no—
187C23×D73—21no—
188#11924028—28no—
189#11924028—44no—
190#11924028—48no—
191#11924027—432no—
192C2×Dic146—21no—
193C2×Dic146—22no—
194C2×Dic146—22no—
195C2×Dic146—22no—
196C2×Dic146—28no—
197C2×Dic146—24no—
198C2×Dic146—21no—
199C2×Dic146—24no—
200C2×Dic146—44no—
201C2×Dic146—48no—
202C2×Dic146—44no—
203C2×Dic146—44no—
204C2×Dic146#4114yescomplemented
205C2×Dic146C2412yes—
206C2×Dic146C2412yes—
207C2×D292—22no—
208C2×D292—22no—
209C2×D292—22no—
210C2×D292—22no—
211C2×D292—21no—
212C2×D292—21no—
213C2×D292C2412yes—
214C2×D292C2412yes—
215C2×C22⋊D73—24no—
216C2×C22⋊D73—24no—
217C2×C22⋊D73—24no—
218C2×C22⋊D73—24no—
219C2×C22⋊D73—44no—
220C2×C22⋊D73—44no—
221C2×C22⋊D73—44no—
222C2×C22⋊D73—44no—
223C22×Dic73—21no—
224C22×Dic73—21no—
225C22×Dic73—21no—
226C22×Dic73—21no—
227C22×Dic73—21no—
228C22×Dic73—21no—
229C22×Dic73—24no—
230C22×Dic73—24no—
231C22×Dic73—24no—
232C22×Dic73—44no—
233C22×Dic73—44no—
234C22×Dic73—44no—
235C2×C4×D73—24no—
236C2×C4×D73—24no—
237C2×C4×D73—44no—
238C2×C4×D73—44no—
239#11924017—28no—
240#11924017—44no—
241D584—44no—
242C4⋊Dic73—21no—
243C4⋊Dic73—21no—
244C4⋊Dic73—21no—
245C4⋊Dic73—24no—
246C4⋊Dic73—24no—
247C4⋊Dic73—24no—
248C4⋊Dic73—21no—
249C4⋊Dic73C2412yes—
250C4⋊Dic73C2412yes—
251C4⋊Dic73C2412yes—
252C4⋊Dic73C2412yes—
253#11924007—24no—
254#11924007—24no—
255C22⋊Dic73—24no—
256#11924005—24no—
257#11924005—24no—
258#11924005—24no—
259#11924005—24no—
260#11924005—24no—
261#11924005—24no—
262C4×Dic73—24no—
263C24×C73C2×D411yescharacteristic
264C24×C73C2×D411yescharacteristic
265C2×D4×C73—24no—
266C2×D4×C73C2×D414yes—
267C22×C4×C73—22no—
268C22×C4×C73—22no—
269C22×C4×C73—22no—
270C22×C4×C73—22no—
271C22×C4×C73C2×D411yescharacteristic
272C22×C4×C73C2×D411yescharacteristic
273C22×C4×C73C2×D411yescharacteristic
274C22×C4×C73C2×D411yescharacteristic
275C22×C4×C73C2×D412yes—
276C22×C4×C73C2×D412yes—
277C22×C4×C73C2412yes—
278C22×C4×C73C2412yes—
279C22×C4×C73C2411yescharacteristic
280M16×C73—44no—
281C2×C8×C73—22no—
282C2×C8×C73—22no—
283C2×C8×C73—22no—
284C2×C8×C73—22no—
285C2×C8×C73—44no—
286C2×C8×C73C2412yes—
287C2×C8×C73C2412yes—
288C2×C8×C73C2412yes—
289C2×C8×C73C2412yes—
290C4⋊C4×C73C2×D414yes—
291C22⋊C4×C73C2×D414yes—
292C22⋊C4×C73C2×D414yes—
293C42×C73C2×D412yes—
294C42×C73C2412yes—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73AGL(1,ℤ/8)14yes—
301C23×C73C22×D412yes—
302C23×C73C22×D412yes—
303C23×C73C22×D411yescharacteristic
304C22×D73—22no—
305C22×D73—22no—
306C22×D73—42no—
307C22×D73—42no—
308C22×D73—42no—
309C22×D73—42no—
310C22×D73—42no—
311C22×D73—42no—
312D4×C73—28no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—24no—
318C2×C4×C73—24no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73C22×D412yes—
324C2×C4×C73C22×D412yes—
325C2×C4×C73C22×D412yes—
326C2×C4×C73C22×D412yes—
327C2×C4×C73C22×D411yescharacteristic
328C2×C4×C73C2×#4112yes—
329C2×C4×C73H(5,𝔽2)12yes—
330C2×C4×C73C2511yescharacteristic
331C22⋊D73—48no—
332C22⋊D73—48no—
333C22⋊D73—48no—
334C22⋊D73—48no—
335C2×Dic73—24no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—48no—
343C2×Dic73—48no—
344C2×Dic73—42no—
345C2×Dic73—42no—
346C2×Dic73—42no—
347C2×Dic73—42no—
348C2×Dic73—48no—
349C2×Dic73—42no—
350D292—22no—
351D292—22no—
352D292—22no—
353D292—22no—
354D292—42no—
355D292—42no—
356C4×D73—48no—
357C4×D73—48no—
358Dic146—24no—
359Dic146—22no—
360Dic146—22no—
361Dic146—22no—
362Dic146—48no—
363Dic146—48no—
364Dic146—42no—
365Dic146C2×#4114yescomplemented
366C8×C73—22no—
367C8×C73—22no—
368C8×C73—22no—
369C8×C73—22no—
370C22×C73—22no—
371C22×C73—28no—
372C22×C73—22no—
373C22×C73—22no—
374C22×C73—22no—
375C22×C73—22no—
376C22×C73—44no—
377C22×C73#54612yes—
378C22×C73C2×AGL(1,ℤ/8)14yes—
379C22×C73C2×AGL(1,ℤ/8)12yes—
380C22×C73#57812yes—
381C22×C73C23×D411yescharacteristic
382C2×D73—42no—
383C2×D73—42no—
384C2×D73—42no—
385C2×D73—42no—
386C2×D73—42no—
387C2×D73—42no—
388C2×D73—84no—
389C2×D73—84no—
390C4×C73—22no—
391C4×C73—22no—
392C4×C73—22no—
393C4×C73—22no—
394C4×C73#54612yes—
395C4×C73C22×#4111yescharacteristic
396C4×C73C2×H(5,𝔽2)11yescharacteristic
397Dic73—24no—
398Dic73—42no—
399Dic73—42no—
400Dic73—42no—
401Dic73—42no—
402Dic73—42no—
403C2×#3308—731nomaximal, Sylow
404C2×C73—24no—
405C2×C73—42no—
406C2×C73#330814yescomplemented
407C2×C73C2×#54611yescharacteristic
408C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
409C2×C73C2×#57811yescharacteristic
410D73—82no—
411D73—82no—
412C2×#548—731no—
413C2×#547—731no—
414#3308—7316no—
415C2×#489—731no—
416C2×#484—731no—
417C2×#480—731no—
418C2×#477—731no—
419C2×#468—731no—
420C2×#466—731no—
421C2×#463—731no—
422C2×#449—731no—
423C2×#448—731no—
424C2×#440—731no—
425C2×#435D7311yescharacteristic, complemented
426C2×#417—731no—
427C22×#103—731no—
428C73C2×#330811yescharacteristic, complemented, Sylow
429C22×#41—731no—
430C22×#41—1461no—
431C23×Q8—731no—
432C22×SD16—731no—
433C22×SD16—731no—
434C22×D8—731no—
435C22×M16C2×D7311yescharacteristic
436C23×C8C2×D7311yescharacteristic
437#548—738no—
438#548—1464no—
439#547—738no—
440#547—1464no—
441C2×C4⋊Q8—731no—
442C2×#124—731no—
443C2×#124—1461no—
444C2×#123—1461no—
445C2×#123—1461no—
446C2×C22⋊Q8—731no—
447C2×C22⋊Q8—1461no—
448C2×C22⋊Q8—1461no—
449C2×#121—731no—
450C2×#121—731no—
451C2×#121—731no—
452C2×#121—1461no—
453C2×C4×Q8—731no—
454C2×C4×D4—731no—
455C2×C4×D4—1461no—
456C2×C4×D4C2×D7311yescharacteristic
457C22×C4⋊C4—731no—
458C22×C4⋊C4—731no—
459#489—738no—
460#484—738no—
461#480—738no—
462#477—738no—
463#468—738no—
464#466—738no—
465#463—738no—
466#449—738no—
467#448—738no—
468#440—738no—
469#435C2×D7318yescomplemented
470C2×#107—731no—
471C2×#107—731no—
472C2×#107—731no—
473C2×C4⋊C8C2×D7311yescharacteristic
474#417—738no—
475C2×#103—731no—
476C2×#103—731no—
477C2×#103—731no—
478C2×#103—731no—
479C2×#103—731no—
480C2×#103—731no—
481C2×#103—738no—
482C2×#102—731no—
483C2×#102—731no—
484C2×#102—731no—
485C2×#102—731no—
486C2×C22⋊C8C2×D7311yescharacteristic
487C2×C22⋊C8C2×D7311yescharacteristic
488C2×#97C2×D7311yescharacteristic
489C2×#41—2922no—
490C2×#41—2928no—
491C2×#41—734no—
492C2×#41—1464no—
493C2×#41—1468no—
494C2×#41—1462no—
495C22×Q8—2922no—
496C22×Q8—734no—
497C22×Q8—731no—
498C22×Q8—731no—
499C22×Q8—1464no—
500C22×Q8—1461no—
501C22×Q8—1461no—
502C22×Q8—1462no—
503C22×D4—731no—
504C22×D4—731no—
505C22×D4—1461no—
506C22×D4—1461no—
507C22×D4—1461no—
508C22×D4—1461no—
509C22×D4D29211yescharacteristic
510C23×C4—1461no—
511C23×C4—1461no—
512C23×C4—1461no—
513C23×C4—1461no—
514C23×C4—1461no—
515C23×C4C22×D7311yescharacteristic
516C23×C4C22×D7311yescharacteristic
517C2×SD16—2922no—
518C2×SD16—734no—
519C2×SD16—734no—
520C2×SD16—1464no—
521C2×D8—2922no—
522C2×D8—734no—
523C2×M16—42no—
524C2×M16C22×D7314yes—
525C22×C8—42no—
526C22×C8C22×D7311yescharacteristic
527C22×C8C22×D7311yescharacteristic
528C22×C8C22×D7311yescharacteristic
529C22×C8C22×D7311yescharacteristic
530C22×C8C22×D7314yes—
531C4⋊Q8—734no—
532C4⋊Q8—1462no—
533#124—734no—
534#124—1468no—
535#124—1462no—
536#123—1468no—
537#123—1468no—
538C22⋊Q8—734no—
539C22⋊Q8—1462no—
540C22⋊Q8—1468no—
541C22⋊Q8—1468no—
542#121—734no—
543#121—734no—
544#121—734no—
545#121—1468no—
546#121—1462no—
547#121—1462no—
548#121—1462no—
549C4×Q8—734no—
550C4×Q8—1462no—
551C4×D4—734no—
552C4×D4—1468no—
553C4×D4—1462no—
554C4×D4D29214yes—
555C4×D4C22×D7314yes—
556C2×C4⋊C4—731no—
557C2×C4⋊C4—731no—
558C2×C4⋊C4—731no—
559C2×C4⋊C4—734no—
560C2×C4⋊C4—734no—
561C2×C4⋊C4—731no—
562C2×C4⋊C4—1461no—
563C2×C4⋊C4—1461no—
564C2×C4⋊C4—1462no—
565C2×C4⋊C4—1462no—
566C2×C4⋊C4—1461no—
567C2×C4⋊C4—1461no—
568C2×C4⋊C4—1461no—
569C2×C4⋊C4D29211yescharacteristic
570C2×C22⋊C4—1461no—
571C2×C22⋊C4—1461no—
572C2×C22⋊C4—1461no—
573C2×C22⋊C4—1461no—
574C2×C22⋊C4—1461no—
575C2×C22⋊C4—1461no—
576C2×C22⋊C4—1461no—
577C2×C22⋊C4D29211yescharacteristic
578C2×C22⋊C4D29211yescharacteristic
579C2×C42—1461no—
580C2×C42C22×D7311yescharacteristic
581#107—734no—
582#107—734no—
583#107—734no—
584C4⋊C8C22×D7314yes—
585#103—734no—
586#103—734no—
587#103—734no—
588#103—734no—
589#103—734no—
590#103—734no—
591#102—734no—
592#102—734no—
593#102—734no—
594#102—734no—
595C22⋊C8C22×D7314yes—
596C22⋊C8C22×D7314yes—
597#97C22×D7314yes—
598C24—1461no—
599C24—1461no—
600C24C2×D29211yescharacteristic
601C24C2×D29211yescharacteristic
602#41—2928no—
603#41—2924no—
604#41—29232no—
605#41—1468no—
606C2×Q8—2924no—
607C2×Q8—2928no—
608C2×Q8—2924no—
609C2×Q8—2924no—
610C2×Q8—734no—
611C2×Q8—732no—
612C2×Q8—732no—
613C2×Q8—1468no—
614C2×Q8—1462no—
615C2×Q8—1462no—
616C2×Q8—1461no—
617C2×Q8—1464no—
618C2×Q8—1464no—
619C2×Q8—1461no—
620C2×Q8—1462no—
621C2×D4—24no—
622C2×D4—2924no—
623C2×D4—2924no—
624C2×D4—2924no—
625C2×D4—2924no—
626C2×D4—732no—
627C2×D4—732no—
628C2×D4—1464no—
629C2×D4—1464no—
630C2×D4—1464no—
631C2×D4—1464no—
632C2×D4—1461no—
633C2×D4—1461no—
634C2×D4—1462no—
635C2×D4—1462no—
636C2×D4—1462no—
637C2×D4—1462no—
638C2×D4C2×D29214yes—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—2924no—
644C22×C4—2924no—
645C22×C4—2924no—
646C22×C4—2924no—
647C22×C4—2924no—
648C22×C4—1464no—
649C22×C4—1464no—
650C22×C4—1464no—
651C22×C4—1461no—
652C22×C4—1461no—
653C22×C4—1461no—
654C22×C4—1461no—
655C22×C4—1461no—
656C22×C4—1464no—
657C22×C4—1464no—
658C22×C4—1461no—
659C22×C4C2×D29212yes—
660C22×C4C2×D29212yes—
661C22×C4C2×D29211yescharacteristic
662C22×C4C2×D29211yescharacteristic
663C22×C4C2×D29211yescharacteristic
664C22×C4C2×D29211yescharacteristic
665C22×C4C23×D7312yes—
666C22×C4C23×D7312yes—
667C22×C4C23×D7311yescharacteristic
668SD16—2924no—
669SD16—1468no—
670D8—2924no—
671M16—44no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8C23×D7312yes—
678C2×C8C23×D7312yes—
679C2×C8C23×D7312yes—
680C2×C8C23×D7312yes—
681C4⋊C4—732no—
682C4⋊C4—732no—
683C4⋊C4—732no—
684C4⋊C4—732no—
685C4⋊C4—1464no—
686C4⋊C4—1464no—
687C4⋊C4—1461no—
688C4⋊C4—1461no—
689C4⋊C4—1461no—
690C4⋊C4—1464no—
691C4⋊C4—1464no—
692C4⋊C4—1461no—
693C4⋊C4—1464no—
694C4⋊C4C2×D29214yes—
695C22⋊C4—1464no—
696C22⋊C4—1464no—
697C22⋊C4—1464no—
698C22⋊C4—1464no—
699C22⋊C4—1464no—
700C22⋊C4—1464no—
701C22⋊C4—1464no—
702C22⋊C4C2×D29214yes—
703C22⋊C4C2×D29214yes—
704C42—1464no—
705C42C2×D29212yes—
706C42C23×D7312yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—2922no—
713C23—2922no—
714C23—2922no—
715C23—2922no—
716C23—2922no—
717C23—2922no—
718C23—1462no—
719C23—1462no—
720C23#1455661914yes—
721C23C22×D29212yes—
722C23C22×D29212yes—
723C23C22×D29211yescharacteristic
724Q8—2928no—
725Q8—2928no—
726Q8—2922no—
727Q8—734no—
728Q8—1462no—
729Q8—1462no—
730Q8—1462no—
731Q8—1464no—
732D4—28no—
733D4—2928no—
734D4—2928no—
735D4—2928no—
736D4—2928no—
737D4—2922no—
738D4—2922no—
739D4—1462no—
740D4—1462no—
741D4—1462no—
742D4—1462no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—2928no—
754C2×C4—2928no—
755C2×C4—2928no—
756C2×C4—2922no—
757C2×C4—2922no—
758C2×C4—2922no—
759C2×C4—2928no—
760C2×C4—2922no—
761C2×C4—2922no—
762C2×C4—2928no—
763C2×C4—1462no—
764C2×C4—1462no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1462no—
769C2×C4—1464no—
770C2×C4C22×D29212yes—
771C2×C4C22×D29212yes—
772C2×C4C22×D29212yes—
773C2×C4C22×D29212yes—
774C2×C4C22×D29211yescharacteristic
775C2×C4#41×D7312yes—
776C2×C4#1455663612yes—
777C2×C4C24×D7311yescharacteristic
778C8—22no—
779C8—22no—
780C8—22no—
781C8—22no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—2922no—
790C22—2922no—
791C22—2922no—
792C22—2922no—
793C22—2922no—
794C22—2922no—
795C22—5844no—
796C22—5844no—
797C22#1798923212yes—
798C22C2×#1455661914yes—
799C22C2×#1455661912yes—
800C22#1798940412yes—
801C22C23×D29211yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—2922no—
807C4—2922no—
808C4—2922no—
809C4—2922no—
810C4—2922no—
811C4—1464no—
812C4#1798923212yes—
813C4C2×#41×D7311yescharacteristic
814C4C2×#1455663611yescharacteristic
815C2—24no—
816C2—42no—
817C2—5842no—
818C2—5842no—
819C2#2262192414yesdirect product factor
820C2C2×#1798923211yescharacteristic
821C2C22×#1455661911yescharacteristic
822C2C2×#1798940411yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#435×C73C2
socleC23×C73C22×D4
hypercenterC2×#435D73
hypocenterC73C2×#3308
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17989246C2semidirect
2. C2×#17989241C2semidirect
3. #22621924C2direct (N × H)
4. C2×#17988947C2semidirect
5. C2×#17988923C2semidirect
6. C2×#17988901C2semidirect
7. C2×#17988883C2semidirect
8. C2×#17988833C2semidirect
9. C2×#17988823C2semidirect
10. C2×#17988803C2semidirect
11. C2×#17988734C2semidirect
12. C2×#17988728C2semidirect
13. C2×#17988689C2semidirect
14. C2×#17988589C2semidirect
15. C22×#14556516C2semidirect
16. C2×#435×C73C2semidirect
24. #17989246C22semidirect
26. #17989241C22semidirect
44. #17988947C22semidirect
45. #17988923C22semidirect
46. #17988901C22semidirect
47. #17988883C22semidirect
48. #17988833C22semidirect
49. #17988823C22semidirect
50. #17988803C22semidirect
51. #17988734C22semidirect
52. #17988728C22semidirect
53. #17988689C22semidirect
57. #17988589C22semidirect
64. C2×#14556516C22semidirect
72. #435×C73C22semidirect
204. C2×Dic146#41semidirect
365. Dic146C2×#41semidirect
406. C2×C73#3308semidirect
425. C2×#435D73semidirect
428. C73C2×#3308semidirect
469. #435C2×D73semidirect
819. C2#22621924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892462
C2×#179892412
#226219242
C2×#179889472
C2×#179889232
C2×#179889012
C2×#179888832
C2×#179888332
C2×#179888232
C2×#179888032
C2×#179887342
C2×#179887282
C2×#179886892
C2×#179885892
C22×#145565162
C2×#435×C732
C2×#330873