Finite Group Databasebeta

← C2×#22621989 #33962597

Subgroups — C2×#22621989 #33962597

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989278C211yesmaximal, characteristic
2C2×#17989252C211yesmaximal, characteristic
3#22621989C2116yesmaximal, direct product factor
4C2×#17988955C211yesmaximal, characteristic, complemented
5C2×#17988927C211yesmaximal, characteristic, complemented
6C2×#17988916C211yesmaximal, characteristic, complemented
7C2×#17988895C211yesmaximal, characteristic, complemented
8C2×#17988842C211yesmaximal, characteristic, complemented
9C2×#17988825C211yesmaximal, characteristic, complemented
10C2×#17988741C211yesmaximal, characteristic, complemented
11C2×#17988741C211yesmaximal, characteristic, complemented
12C2×#17988692C211yesmaximal, characteristic, complemented
13C2×#17988657C211yesmaximal, characteristic
14C2×#17988594C211yesmaximal, characteristic, complemented
15C2×#103×D73C211yesmaximal, characteristic, complemented
16C2×#462×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924011C2211yescharacteristic
21C22×C8×D73C2211yescharacteristic
22#17989278—24no—
23#17989278C2218yes—
24#17989252—24no—
25#17989252C2218yes—
26C2×#14556590—21no—
27C2×#14556585—21no—
28C2×#14556583C2211yescharacteristic
29C2×#14556581—21no—
30C2×#14556576—21no—
31C2×#14556569—21no—
32C2×#14556569—21no—
33C2×#14556567C2211yescharacteristic
34C2×#14556567C2211yescharacteristic
35C2×#14556567C2211yescharacteristic
36C2×#14556567C2211yescharacteristic
37C2×C4×Dic146C2211yescharacteristic
38C2×C4×D292C2211yescharacteristic
39C2×#14556553—21no—
40C2×#14556549C2211yescharacteristic
41C2×#14556548—21no—
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988955C2218yescomplemented
44#17988927C2218yescomplemented
45#17988916C2218yescomplemented
46#17988895C2218yescomplemented
47#17988842C2218yescomplemented
48#17988825C2218yescomplemented
49#17988741C2218yescomplemented
50#17988741C2218yescomplemented
51#17988692C2218yescomplemented
52#17988657C2218yes—
53C2×#14556525C2211yescharacteristic
54C2×#14556523C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56#17988594C2218yescomplemented
57C2×#14556516C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65#103×D73C2218yescomplemented
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556502C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C2×C4⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#462×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C2×Q8×D73—22no—
81C2×Q8×D73—22no—
82C2×Q8×D73—24no—
83C2×Q8×D73—24no—
84C2×Q8×D73—42no—
85C2×Q8×D73—42no—
86C2×Q8×D73C2314yes—
87C2×Q8×D73C2314yes—
88C22×D292D411yescharacteristic
89C22×C4×D73—21no—
90C22×C4×D73—21no—
91C22×C4×D73—21no—
92C22×C4×D73C2311yescharacteristic
93C22×C4×D73C2311yescharacteristic
94C2×#11924018—24no—
95C2×#11924018C2314yes—
96C2×#11924011—42no—
97C2×#11924011C2314yes—
98C22×#10596831C2311yescharacteristic
99C22×#10596831C2311yescharacteristic
100C2×C8×D73—42no—
101C2×C8×D73C2314yes—
102#14556590—28no—
103#14556585—28no—
104#14556583—22no—
105#14556583C2314yes—
106#14556581—28no—
107#14556576—28no—
108#14556569—28no—
109#14556569—28no—
110#14556567—22no—
111#14556567—22no—
112#14556567—22no—
113#14556567—22no—
114#14556567C2314yes—
115#14556567C2314yes—
116#14556567C2314yes—
117#14556567C2314yes—
118C4×Dic146—22no—
119C4×Dic146C2314yes—
120C4×D292D414yes—
121C4×D292C2314yes—
122#14556553—28no—
123#14556549—22no—
124#14556549C2314yes—
125#14556548—28no—
126C2×C4⋊Dic73D411yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C4⋊C4×D73—22no—
139C4⋊C4×D73C2314yes—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005D411yescharacteristic
146C2×#11924005D411yescharacteristic
147C2×C4×Dic73—21no—
148C2×C4×Dic73—21no—
149#14556525C2314yes—
150#14556523C2314yes—
151#14556522C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556515C2314yes—
156#14556515C2314yes—
157#14556515C2314yes—
158#14556515C2314yes—
159#14556514C2314yes—
160#14556503C2314yes—
161#14556503C2314yes—
162#14556502C2314yes—
163C22×Q8×C73C2311yescharacteristic
164C22×Q8×C73C2311yescharacteristic
165C22×Q8×C73C2311yescharacteristic
166C2×Q16×C73—42no—
167C2×Q16×C73—42no—
168C2×Q16×C73C2314yes—
169C2×Q16×C73C2314yes—
170C22×C8×C73C2311yescharacteristic
171C22×C8×C73C2311yescharacteristic
172C4⋊Q8×C73—22no—
173C4⋊Q8×C73C2314yes—
174C4×Q8×C73—22no—
175C4×Q8×C73C2314yes—
176C2×C4⋊C4×C73—21no—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73—21no—
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C42×C73—21no—
181C2×C42×C73C2311yescharacteristic
182C4⋊C8×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186C23×D73C2×D411yescharacteristic
187C2×Dic146—21no—
188C2×Dic146—22no—
189C2×Dic146—24no—
190C2×Dic146—24no—
191C2×Dic146—44no—
192C2×Dic146—44no—
193C2×Dic146#4114yes—
194C2×Dic146C2412yes—
195Q8×D73—28no—
196Q8×D73—28no—
197Q8×D73—44no—
198Q8×D73—44no—
199Q8×D73—48no—
200Q8×D73—48no—
201C2×D292—24no—
202C2×D292C2×D414yes—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C2×C4×D73—22no—
210C2×C4×D73—22no—
211C2×C4×D73—22no—
212C2×C4×D73—22no—
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—24no—
216C2×C4×D73—44no—
217C2×C4×D73—44no—
218C2×C4×D73—44no—
219C2×C4×D73C2×D412yes—
220C2×C4×D73C2×D412yes—
221C2×C4×D73C2412yes—
222C2×C4×D73C2412yes—
223#11924018—28no—
224#11924011—44no—
225C2×#10596831—22no—
226C2×#10596831—22no—
227C2×#10596831C2412yes—
228C2×#10596831C2412yes—
229C8×D73—44no—
230C4⋊Dic73—21no—
231C4⋊Dic73—21no—
232C4⋊Dic73—21no—
233C4⋊Dic73C2×D414yes—
234C4⋊Dic73C2412yes—
235C4⋊Dic73C2412yes—
236C4⋊Dic73C2412yes—
237#11924007—24no—
238#11924007—24no—
239#11924007—24no—
240#11924007—24no—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924005—24no—
246#11924005—24no—
247#11924005—24no—
248#11924005—24no—
249#11924005—24no—
250#11924005C2×D414yes—
251#11924005C2×D414yes—
252C4×Dic73—24no—
253C4×Dic73—24no—
254C2×Q8×C73—21no—
255C2×Q8×C73—21no—
256C2×Q8×C73—21no—
257C2×Q8×C73—22no—
258C2×Q8×C73—22no—
259C2×Q8×C73—22no—
260C2×Q8×C73—22no—
261C2×Q8×C73—22no—
262C2×Q8×C73—22no—
263C2×Q8×C73C2412yes—
264C2×Q8×C73C2412yes—
265C2×Q8×C73C2412yes—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73C2×D411yescharacteristic
271C22×C4×C73C2×D411yescharacteristic
272C22×C4×C73C2411yescharacteristic
273Q16×C73—44no—
274Q16×C73—44no—
275C2×C8×C73—22no—
276C2×C8×C73—22no—
277C2×C8×C73C2412yes—
278C2×C8×C73C2412yes—
279C4⋊C4×C73—24no—
280C4⋊C4×C73—24no—
281C4⋊C4×C73—24no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73C2412yes—
284C42×C73—24no—
285C42×C73C2×D412yes—
286C42×C73C2412yes—
287C23×C73C22×D411yescharacteristic
288C22×D73—22no—
289C22×D73—22no—
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—22no—
293C22×D73#13714yes—
294C22×D73C22×D412yes—
295C22×D73C22×D412yes—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73—22no—
299Q8×C73—22no—
300Q8×C73—22no—
301Q8×C73—22no—
302Q8×C73—42no—
303Q8×C73—42no—
304Q8×C73—42no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—42no—
312C2×C4×C73—42no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73C22×D412yes—
316C2×C4×C73C22×D412yes—
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C2×#4112yes—
319C2×C4×C73H(5,𝔽2)12yes—
320C2×C4×C73C2511yescharacteristic
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—24no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333D292—28no—
334C4×D73—24no—
335C4×D73—24no—
336C4×D73—22no—
337C4×D73—22no—
338C4×D73—22no—
339C4×D73—22no—
340C4×D73—48no—
341C4×D73—48no—
342C4×D73—48no—
343Dic146—24no—
344Dic146—22no—
345Dic146—48no—
346Dic146—48no—
347Dic146C2×#4114yes—
348C8×C73—22no—
349C8×C73—22no—
350#10596831—22no—
351#10596831—22no—
352C22×C73#54612yes—
353C22×C73C2×#13712yes—
354C22×C73#57812yes—
355C22×C73C23×D411yescharacteristic
356C2×D73—22no—
357C2×D73—28no—
358C2×D73—22no—
359C2×D73—22no—
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—44no—
363C2×D73C2×#13714yes—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73—42no—
369C4×C73—42no—
370C4×C73#54612yes—
371C4×C73C22×#4111yescharacteristic
372C4×C73C2×H(5,𝔽2)11yescharacteristic
373Dic73—24no—
374Dic73—22no—
375Dic73—22no—
376Dic73—42no—
377Dic73—42no—
378Dic73—42no—
379C2×#3312—731nomaximal, Sylow
380C2×C73#331214yescomplemented
381C2×C73C2×#54611yescharacteristic
382C2×C73C22×#13711yescharacteristic
383C2×C73C2×#57811yescharacteristic
384D73—24no—
385D73—42no—
386C2×#552—731no—
387C2×D4×Q8—731no—
388#3312—7316no—
389C2×#491—731no—
390C2×#485—731no—
391C2×#483—731no—
392C2×#479—731no—
393C2×#470—731no—
394C2×#467—731no—
395C2×#462D7311yescharacteristic, complemented
396C2×#451—731no—
397C2×#451—731no—
398C2×#441—731no—
399C2×#435—731no—
400C2×#419—731no—
401C22×#103—731no—
402C73C2×#331211yescharacteristic, complemented, Sylow
403C23×Q8—731no—
404C23×Q8—731no—
405C22×Q16—731no—
406C22×Q16C2×D7311yescharacteristic
407C22×Q16C2×D7311yescharacteristic
408C22×M16—731no—
409C23×C8—731no—
410#552—738no—
411#552—1464no—
412D4×Q8—738no—
413D4×Q8—1464no—
414C2×C4⋊Q8—1461no—
415C2×C4⋊Q8C2×D7311yescharacteristic
416C2×#126—1461no—
417C2×#125—731no—
418C2×#125—1461no—
419C2×#123—1461no—
420C2×C22⋊Q8—731no—
421C2×C22⋊Q8—731no—
422C2×C22⋊Q8—731no—
423C2×C22⋊Q8—731no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8—1461no—
426C2×C4×Q8—731no—
427C2×C4×Q8C2×D7311yescharacteristic
428C2×C4×D4—731no—
429C2×C4×D4—1461no—
430C2×#117—731no—
431C2×#117—1461no—
432C22×C4⋊C4—731no—
433#491—738no—
434#485—738no—
435#483—738no—
436#479—738no—
437#470—738no—
438#467—738no—
439#462C2×D7318yescomplemented
440#451—738no—
441#451—738no—
442#441—738no—
443#435—738no—
444C2×#107—731no—
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8C2×D7311yescharacteristic
448#419—738no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103—731no—
457C2×#103—738no—
458C2×#103C2×D7311yescharacteristic
459C2×#103C2×D7311yescharacteristic
460C2×C22⋊C8—731no—
461C2×C22⋊C8—731no—
462C2×#97—731no—
463C22×Q8—2922no—
464C22×Q8—2922no—
465C22×Q8—734no—
466C22×Q8—734no—
467C22×Q8—731no—
468C22×Q8—1461no—
469C22×Q8—1461no—
470C22×Q8—1464no—
471C22×Q8—1464no—
472C22×Q8—1462no—
473C22×Q8—1462no—
474C22×Q8C22×D7311yescharacteristic
475C22×Q8C22×D7311yescharacteristic
476C22×Q8C22×D7311yescharacteristic
477C22×D4—731no—
478C23×C4—731no—
479C23×C4—731no—
480C23×C4—1461no—
481C23×C4—1461no—
482C23×C4—1461no—
483C2×Q16—42no—
484C2×Q16—42no—
485C2×Q16—734no—
486C2×Q16—1464no—
487C2×Q16C22×D7314yes—
488C2×Q16C22×D7314yes—
489C2×M16—2922no—
490C2×M16—734no—
491C22×C8—2922no—
492C22×C8—734no—
493C22×C8—731no—
494C22×C8—731no—
495C22×C8C22×D7311yescharacteristic
496C22×C8C22×D7311yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—1468no—
499C4⋊Q8C22×D7314yes—
500#126—1468no—
501#125—734no—
502#125—1468no—
503#125—1462no—
504#123—1468no—
505C22⋊Q8—734no—
506C22⋊Q8—734no—
507C22⋊Q8—734no—
508C22⋊Q8—734no—
509C22⋊Q8—1468no—
510C22⋊Q8—1468no—
511C22⋊Q8—1462no—
512C22⋊Q8—1462no—
513C22⋊Q8—1462no—
514C22⋊Q8—1462no—
515C4×Q8—22no—
516C4×Q8—734no—
517C4×Q8—1462no—
518C4×Q8C22×D7314yes—
519C4×D4—734no—
520C4×D4—734no—
521C4×D4—1468no—
522#117—734no—
523#117—1468no—
524#117—1462no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—731no—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—734no—
533C2×C4⋊C4—1462no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1461no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4C22×D7311yescharacteristic
543C2×C22⋊C4—731no—
544C2×C22⋊C4—731no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C22⋊C4—1461no—
548C2×C22⋊C4—1461no—
549C2×C22⋊C4—1461no—
550C2×C42—21no—
551C2×C42—1461no—
552C2×C42—1461no—
553C2×C42C22×D7311yescharacteristic
554#107—734no—
555#106—734no—
556#106—734no—
557C4⋊C8C22×D7314yes—
558#103—734no—
559#103—734no—
560#103—734no—
561#103—734no—
562#103—734no—
563#103—734no—
564#103—734no—
565#103—734no—
566#103C22×D7314yes—
567#103C22×D7314yes—
568C22⋊C8—734no—
569C22⋊C8—734no—
570#97—734no—
571C24—731no—
572C24—731no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—2924no—
583C2×Q8—2924no—
584C2×Q8—2924no—
585C2×Q8—2924no—
586C2×Q8—2928no—
587C2×Q8—2928no—
588C2×Q8—734no—
589C2×Q8—732no—
590C2×Q8—1464no—
591C2×Q8—1464no—
592C2×Q8—1468no—
593C2×Q8—1468no—
594C2×Q8—1461no—
595C2×Q8—1462no—
596C2×Q8C23×D7312yes—
597C2×Q8C23×D7312yes—
598C2×Q8C23×D7312yes—
599C2×D4—734no—
600C2×D4—1464no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—2924no—
606C22×C4—2924no—
607C22×C4—2924no—
608C22×C4—731no—
609C22×C4—731no—
610C22×C4—732no—
611C22×C4—732no—
612C22×C4—732no—
613C22×C4—732no—
614C22×C4—1464no—
615C22×C4—1464no—
616C22×C4—1464no—
617C22×C4—1461no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1462no—
622C22×C4—1462no—
623C22×C4—1462no—
624C22×C4—1462no—
625C22×C4D4×D7311yescharacteristic
626C22×C4D4×D7311yescharacteristic
627C22×C4C23×D7311yescharacteristic
628Q16—44no—
629Q16—44no—
630Q16—1468no—
631M16—2924no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—2924no—
635C2×C8—732no—
636C2×C8—732no—
637C2×C8—1462no—
638C2×C8—1462no—
639C2×C8C23×D7312yes—
640C2×C8C23×D7312yes—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—734no—
646C4⋊C4—732no—
647C4⋊C4—732no—
648C4⋊C4—732no—
649C4⋊C4—1464no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1464no—
655C4⋊C4—1464no—
656C4⋊C4—1464no—
657C4⋊C4—1461no—
658C4⋊C4—1461no—
659C4⋊C4—1461no—
660C4⋊C4C23×D7312yes—
661C22⋊C4—734no—
662C22⋊C4—734no—
663C22⋊C4—1464no—
664C22⋊C4—1464no—
665C22⋊C4—1464no—
666C22⋊C4—1464no—
667C22⋊C4—1464no—
668C42—24no—
669C42—1464no—
670C42—1464no—
671C42D4×D7312yes—
672C42C23×D7312yes—
673C23—734no—
674C23—732no—
675C23—732no—
676C23—1462no—
677C23—1462no—
678C23—1462no—
679C23—1462no—
680C23—1462no—
681C23C2×D4×D7311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—2928no—
692Q8—2928no—
693Q8—734no—
694Q8—1462no—
695Q8—1464no—
696D4—1468no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—2928no—
708C2×C4—2928no—
709C2×C4—2928no—
710C2×C4—2922no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—732no—
714C2×C4—732no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1464no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1464no—
727C2×C4—1464no—
728C2×C4C2×D4×D7312yes—
729C2×C4C2×D4×D7312yes—
730C2×C4C2×D4×D7311yescharacteristic
731C2×C4#41×D7312yes—
732C2×C4#1455663612yes—
733C2×C4C24×D7311yescharacteristic
734C8—22no—
735C8—22no—
736C8—1462no—
737C8—1462no—
738C22—2924no—
739C22—734no—
740C22—1462no—
741C22—1462no—
742C22—1462no—
743C22—1468no—
744C22—1462no—
745C22—1462no—
746C22#1798923412yes—
747C22#137×D7312yes—
748C22#1798940012yes—
749C22C22×D4×D7311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—2922no—
757C4—2922no—
758C4—2922no—
759C4—1464no—
760C4—1462no—
761C4—1462no—
762C4#1798923412yes—
763C4C2×#41×D7311yescharacteristic
764C4C2×#1455663611yescharacteristic
765C2—2922no—
766C2—1464no—
767C2#2262198914yesdirect product factor
768C2C2×#1798923411yescharacteristic
769C2C2×#137×D7311yescharacteristic
770C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#462×C73C2
socleC23×C73C22×D4
prime radicalC22×D292D4
hypercenterC2×#462D73
hypocenterC73C2×#3312
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #22621989C2direct (N × H)
4. C2×#17988955C2semidirect
5. C2×#17988927C2semidirect
6. C2×#17988916C2semidirect
7. C2×#17988895C2semidirect
8. C2×#17988842C2semidirect
9. C2×#17988825C2semidirect
10. C2×#17988741C2semidirect
11. C2×#17988741C2semidirect
12. C2×#17988692C2semidirect
14. C2×#17988594C2semidirect
15. C2×#103×D73C2semidirect
16. C2×#462×C73C2semidirect
43. #17988955C22semidirect
44. #17988927C22semidirect
45. #17988916C22semidirect
46. #17988895C22semidirect
47. #17988842C22semidirect
48. #17988825C22semidirect
49. #17988741C22semidirect
50. #17988741C22semidirect
51. #17988692C22semidirect
56. #17988594C22semidirect
65. #103×D73C22semidirect
73. #462×C73C22semidirect
380. C2×C73#3312semidirect
395. C2×#462D73semidirect
402. C73C2×#3312semidirect
439. #462C2×D73semidirect
767. C2#22621989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892782
C2×#179892522
#226219892
C2×#179889552
C2×#179889272
C2×#179889162
C2×#179888952
C2×#179888422
C2×#179888252
C2×#179887412
C2×#179886922
C2×#179886572
C2×#179885942
C2×#103×D732
C2×#462×C732
C2×#331273