Finite Group Databasebeta

← C2×#22618876 #33950362

Subgroups — C2×#22618876 #33950362

Order 18688.

1938 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic
2#22618876C2116yesmaximal, direct product factor
3C2×#17988718C211yesmaximal, characteristic, complemented
4C2×#17988716C211yesmaximal, characteristic, complemented
5C2×#17988716C211yesmaximal, characteristic, complemented
6C2×#17988715C211yesmaximal, characteristic, complemented
7C2×#17988715C211yesmaximal, characteristic, complemented
8C2×C8×Dic146C211yesmaximal, characteristic, complemented
9C2×#17988711C211yesmaximal, characteristic, complemented
10C2×#17988612C211yesmaximal, characteristic
11C2×#17988612C211yesmaximal, characteristic
12C2×C4⋊C8×D73C211yesmaximal, characteristic
13C2×#17988544C211yesmaximal, characteristic
14C2×#17988541C211yesmaximal, characteristic
15C2×#17988539C211yesmaximal, characteristic
16C2×#446×C73C211yesmaximal, characteristic, complemented
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989141C418yes—
22#17989141C2218yes—
23C2×#14556590C411yescharacteristic
24C2×#14556589C411yescharacteristic
25C2×#14556581C411yescharacteristic
26C2×#14556581C411yescharacteristic
27C2×#14556571C411yescharacteristic
28C2×#14556569C411yescharacteristic
29C2×#14556569C411yescharacteristic
30C2×#14556567C411yescharacteristic
31C2×C4×Dic146C2211yescharacteristic
32C2×C4×Dic146C2211yescharacteristic
33C2×C4×Dic146C2211yescharacteristic
34C2×#14556548C2211yescharacteristic
35C2×#14556548C2211yescharacteristic
36C2×C42×D73C2211yescharacteristic
37#17988718C2218yescomplemented
38#17988716C2218yescomplemented
39#17988716C2218yescomplemented
40#17988715C2218yescomplemented
41#17988715C2218yescomplemented
42C8×Dic146C2218yescomplemented
43#17988711C2218yescomplemented
44#17988612C2218yes—
45#17988612C2218yes—
46C2×C4⋊#10596831C2211yescharacteristic
47C2×C4⋊#10596831C2211yescharacteristic
48C2×C4⋊#10596831C2211yescharacteristic
49C2×#14556520C2211yescharacteristic
50C2×#14556520C2211yescharacteristic
51C2×#14556520C2211yescharacteristic
52C2×#14556520C2211yescharacteristic
53C2×#14556520C2211yescharacteristic
54C2×#14556520C2211yescharacteristic
55C4⋊C8×D73C2218yes—
56#17988544C2218yes—
57#17988541C2218yes—
58#17988539C2218yes—
59C2×#14556502C2211yescharacteristic
60C2×#14556502C2211yescharacteristic
61C2×#14556501C2211yescharacteristic
62C2×#14556501C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64C2×C8×Dic73C2211yescharacteristic
65C2×C8×Dic73C2211yescharacteristic
66C2×C8×Dic73C2211yescharacteristic
67C2×C8×Dic73C2211yescharacteristic
68C2×C4×Q8×C73C2211yescharacteristic
69#446×C73C2218yescomplemented
70C2×C4⋊C8×C73C2211yescharacteristic
71C2×C4⋊C8×C73C2211yescharacteristic
72C2×C4⋊C8×C73C2211yescharacteristic
73C2×#97×C73C2211yescharacteristic
74C2×#97×C73C2211yescharacteristic
75C2×C4×C8×C73C2211yescharacteristic
76C22×Dic146C2×C411yescharacteristic
77C22×Dic146C2×C411yescharacteristic
78C22×Dic146C2×C411yescharacteristic
79C22×C4×D73C2×C411yescharacteristic
80C22×C4×D73C2×C411yescharacteristic
81C22×C4×D73C2311yescharacteristic
82C2×#11924011—24no—
83C2×#11924011Q818yescomplemented
84C2×#11924011C2314yes—
85C2×#11924011C2314yes—
86C22×#10596831C2311yescharacteristic
87C22×#10596831C2311yescharacteristic
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90C2×C8×D73—24no—
91C2×C8×D73—24no—
92C2×C8×D73C2314yes—
93C2×C8×D73C2314yes—
94#14556590C2×C418yes—
95#14556589C2×C418yes—
96#14556581C2×C418yes—
97#14556581C2×C418yes—
98#14556571C2×C418yes—
99#14556569C2×C418yes—
100#14556569C2×C418yes—
101#14556567C2×C418yes—
102C4×Dic146C2×C414yes—
103C4×Dic146C2×C414yes—
104C4×Dic146C2×C414yes—
105C4×Dic146C2314yes—
106C4×Dic146C2314yes—
107C4×Dic146C2314yes—
108#14556548C2×C414yes—
109#14556548C2×C414yes—
110#14556548C2314yes—
111#14556548C2314yes—
112C2×C4⋊Dic73C2×C411yescharacteristic
113C2×C4⋊Dic73C2×C411yescharacteristic
114C2×C4⋊Dic73C2×C411yescharacteristic
115C2×#11924007C2×C411yescharacteristic
116C2×#11924007C2×C411yescharacteristic
117C2×#11924007C2×C411yescharacteristic
118C2×#11924007C2×C411yescharacteristic
119C2×#11924007C2×C411yescharacteristic
120C2×#11924007C2×C411yescharacteristic
121C2×#11924007C2×C411yescharacteristic
122C2×#11924007C2×C411yescharacteristic
123C2×#11924007C2×C411yescharacteristic
124C2×#11924007C2×C411yescharacteristic
125C2×#11924005C2×C411yescharacteristic
126C2×#11924005C2×C411yescharacteristic
127C2×#11924005C2×C411yescharacteristic
128C2×#11924005C2×C411yescharacteristic
129C2×C4×Dic73C2×C411yescharacteristic
130C2×C4×Dic73C2×C411yescharacteristic
131C2×C4×Dic73C2311yescharacteristic
132C2×C4×Dic73C2311yescharacteristic
133C2×C4×Dic73C2311yescharacteristic
134C42×D73C2×C414yes—
135C42×D73C2314yes—
136C4⋊#10596831C2314yes—
137C4⋊#10596831C2314yes—
138C4⋊#10596831C2314yes—
139#14556520C2314yes—
140#14556520C2314yes—
141#14556520C2314yes—
142#14556520C2314yes—
143#14556520C2314yes—
144#14556520C2314yes—
145#14556502C2314yes—
146#14556502C2314yes—
147#14556501C2314yes—
148#14556501C2314yes—
149C4×#10596831C2314yes—
150C8×Dic73C2314yes—
151C8×Dic73C2314yes—
152C8×Dic73C2314yes—
153C8×Dic73C2314yes—
154C22×Q8×C73C2×C411yescharacteristic
155C22×C8×C73C2311yescharacteristic
156C22×C8×C73C2311yescharacteristic
157C22×C8×C73C2311yescharacteristic
158C22×C8×C73C2311yescharacteristic
159C4×Q8×C73C2×C414yes—
160C4×Q8×C73C2314yes—
161C2×C4⋊C4×C73C2×C411yescharacteristic
162C2×C4⋊C4×C73C2×C411yescharacteristic
163C2×C4⋊C4×C73C2×C411yescharacteristic
164C2×C42×C73C2311yescharacteristic
165C2×C42×C73C2311yescharacteristic
166C2×C42×C73C2311yescharacteristic
167C4⋊C8×C73C2314yes—
168C4⋊C8×C73C2314yes—
169C4⋊C8×C73C2314yes—
170#97×C73C2314yes—
171#97×C73C2314yes—
172C4×C8×C73C2314yes—
173C23×D73C22×C411yescharacteristic
174C2×Dic146—24no—
175C2×Dic146—24no—
176C2×Dic146—42no—
177C2×Dic146C22×C414yes—
178C2×Dic146C22×C414yes—
179C2×Dic146C22×C414yes—
180C22×Dic73C22×C411yescharacteristic
181C22×Dic73C22×C411yescharacteristic
182C22×Dic73C22×C411yescharacteristic
183C22×Dic73C22×C411yescharacteristic
184C22×Dic73C22×C411yescharacteristic
185C22×Dic73C22×C411yescharacteristic
186C22×Dic73C22×C411yescharacteristic
187C2×C4×D73—24no—
188C2×C4×D73—42no—
189C2×C4×D73C22×C414yes—
190C2×C4×D73C22×C414yes—
191C2×C4×D73C22×C412yes—
192C2×C4×D73C2×Q814yes—
193C2×C4×D73#4114yes—
194C2×C4×D73C2412yes—
195#11924011—28no—
196#11924011C2×Q8116yescomplemented
197C2×#10596831—22no—
198C2×#10596831—22no—
199C2×#10596831—22no—
200C2×#10596831C2×Q814yes—
201C2×#10596831C2412yes—
202C2×#10596831C2412yes—
203C2×#10596831C2412yes—
204C2×#10596831C2412yes—
205C8×D73—28no—
206C8×D73—28no—
207C4⋊Dic73C22×C414yes—
208C4⋊Dic73C22×C414yes—
209C4⋊Dic73C22×C414yes—
210#11924007C22×C414yes—
211#11924007C22×C414yes—
212#11924007C22×C414yes—
213#11924007C22×C414yes—
214#11924007C22×C414yes—
215#11924007C22×C414yes—
216#11924007C22×C414yes—
217#11924007C22×C414yes—
218#11924007C22×C414yes—
219#11924007C22×C414yes—
220#11924005C22×C414yes—
221#11924005C22×C414yes—
222#11924005C22×C414yes—
223#11924005C22×C414yes—
224C4×Dic73C22×C412yes—
225C4×Dic73C22×C414yes—
226C4×Dic73C22×C414yes—
227C4×Dic73C22×C412yes—
228C4×Dic73C22×C412yes—
229C4×Dic73C2412yes—
230C4×Dic73C2412yes—
231C4×Dic73C2412yes—
232C2×Q8×C73—42no—
233C2×Q8×C73C22×C414yes—
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C22×C411yescharacteristic
239C22×C4×C73C22×C411yescharacteristic
240C22×C4×C73C2411yescharacteristic
241C2×C8×C73—22no—
242C2×C8×C73—22no—
243C2×C8×C73—22no—
244C2×C8×C73C2×Q814yes—
245C2×C8×C73C2412yes—
246C2×C8×C73C2412yes—
247C2×C8×C73C2412yes—
248C2×C8×C73C2412yes—
249C4⋊C4×C73C22×C414yes—
250C4⋊C4×C73C22×C414yes—
251C4⋊C4×C73C22×C414yes—
252C42×C73C22×C412yes—
253C42×C73C22×C412yes—
254C42×C73C22×C412yes—
255C42×C73C2412yes—
256C42×C73C2412yes—
257C42×C73C2412yes—
258C23×C73C23×C411yescharacteristic
259C22×D73—22no—
260C22×D73—22no—
261C22×D73C4×Q814yes—
262C22×D73C23×C412yes—
263Q8×C73—44no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73C23×C412yes—
271C2×C4×C73C23×C412yes—
272C2×C4×C73C23×C412yes—
273C2×C4×C73C23×C412yes—
274C2×C4×C73C23×C412yes—
275C2×C4×C73C23×C412yes—
276C2×C4×C73C23×C411yescharacteristic
277C2×C4×C73C22×Q812yes—
278C2×C4×C73C2×#4112yes—
279C2×C4×C73C2511yescharacteristic
280C2×Dic73—22no—
281C2×Dic73—22no—
282C2×Dic73—22no—
283C2×Dic73—22no—
284C2×Dic73—22no—
285C2×Dic73C4×Q814yes—
286C2×Dic73#13114yes—
287C2×Dic73C23×C412yes—
288C2×Dic73C23×C412yes—
289C2×Dic73C23×C412yes—
290C2×Dic73C23×C412yes—
291C2×Dic73C23×C412yes—
292C2×Dic73C23×C412yes—
293C2×Dic73C23×C412yes—
294C4×D73—28no—
295C4×D73—44no—
296C4×D73C4×Q818yes—
297C4×D73C22×Q814yes—
298C4×D73C2×#4114yes—
299Dic146—28no—
300Dic146—28no—
301Dic146—44no—
302C8×C73—22no—
303C8×C73—22no—
304C8×C73—22no—
305C8×C73C22×Q814yes—
306#10596831—22no—
307#10596831—22no—
308#10596831—22no—
309#10596831C22×Q814yes—
310C22×C73C2×C4×Q812yes—
311C22×C73C2×#13112yes—
312C22×C73#56812yes—
313C22×C73C24×C411yescharacteristic
314C2×D73—28no—
315C2×D73—22no—
316C2×D73—22no—
317C2×D73C2×C4×Q814yes—
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—22no—
321C4×C73—22no—
322C4×C73—22no—
323C4×C73—22no—
324C4×C73C2×C4×Q812yes—
325C4×C73C23×Q811yescharacteristic
326C4×C73C22×#4111yescharacteristic
327Dic73—22no—
328Dic73—22no—
329Dic73—22no—
330Dic73—22no—
331Dic73—22no—
332Dic73C2×C4×Q814yes—
333Dic73C2×#13114yes—
334C2×#2962—731nomaximal, Sylow
335C2×C73#296214yescomplemented
336C2×C73C22×C4×Q811yescharacteristic
337C2×C73C22×#13111yescharacteristic
338C2×C73C2×#56811yescharacteristic
339D73—24no—
340C2×#533—731no—
341#2962—7316no—
342C2×#446—731no—
343C2×#446—731no—
344C2×#446—731no—
345C2×#446—731no—
346C2×#446—731no—
347C2×#446D7311yescharacteristic, complemented
348C2×C8×Q8—731no—
349C2×C8×Q8—731no—
350C2×#424—731no—
351C2×#424—731no—
352C22×C4⋊C8—731no—
353C2×#405—731no—
354C2×#405—731no—
355C2×C4×M16—731no—
356C73C2×#296211yescharacteristic, complemented, Sylow
357C22×M16—731no—
358C22×M16—731no—
359C23×C8—731no—
360C23×C8—731no—
361#533—738no—
362#533—738no—
363C2×C4⋊Q8—731no—
364C2×C4⋊Q8—731no—
365C2×#125—731no—
366C2×#125—731no—
367C2×C22⋊Q8—731no—
368C2×C22⋊Q8—731no—
369C2×C22⋊Q8—731no—
370C2×C22⋊Q8—731no—
371C2×C4×Q8—731no—
372C2×C4×Q8—731no—
373C2×C4×Q8—731no—
374C2×C4×Q8C2×D7311yescharacteristic
375C2×#117—731no—
376C2×#117—731no—
377C22×C42—731no—
378#446—738no—
379#446—738no—
380#446—738no—
381#446—738no—
382#446—738no—
383#446C2×D7318yescomplemented
384C8×Q8—738no—
385C8×Q8—738no—
386#424—738no—
387#424—738no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×C4⋊C8—731no—
393C2×C4⋊C8—731no—
394C2×C4⋊C8—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8—738no—
398C2×C4⋊C8C2×D7311yescharacteristic
399C2×C4⋊C8C2×D7311yescharacteristic
400C2×C4⋊C8C2×D7311yescharacteristic
401#405—738no—
402#405—738no—
403C4×M16—738no—
404C2×#97—731no—
405C2×#97—731no—
406C2×#97—731no—
407C2×#97—731no—
408C2×#97C2×D7311yescharacteristic
409C2×#97C2×D7311yescharacteristic
410C2×C4×C8—731no—
411C2×C4×C8—731no—
412C2×C4×C8—731no—
413C2×C4×C8—731no—
414C2×C4×C8—731no—
415C2×C4×C8C2×D7311yescharacteristic
416C22×Q8—731no—
417C22×Q8—731no—
418C22×Q8—731no—
419C22×Q8C4×D7311yescharacteristic
420C23×C4—731no—
421C23×C4—731no—
422C23×C4—731no—
423C2×M16—738no—
424C2×M16—734no—
425C2×M16—734no—
426C2×M16—1464no—
427C22×C8—731no—
428C22×C8—731no—
429C22×C8—731no—
430C22×C8—731no—
431C22×C8—734no—
432C22×C8—734no—
433C22×C8—1464no—
434C22×C8—1464no—
435C22×C8C22×D7311yescharacteristic
436C22×C8C22×D7311yescharacteristic
437C22×C8C22×D7311yescharacteristic
438C22×C8C22×D7311yescharacteristic
439C4⋊Q8—738no—
440C4⋊Q8—738no—
441#125—738no—
442#125—738no—
443C22⋊Q8—738no—
444C22⋊Q8—738no—
445C22⋊Q8—738no—
446C22⋊Q8—738no—
447C4×Q8—734no—
448C4×Q8—734no—
449C4×Q8—734no—
450C4×Q8—734no—
451C4×Q8—734no—
452C4×Q8—734no—
453C4×Q8C4×D7314yes—
454C4×Q8C22×D7314yes—
455#117—734no—
456#117—734no—
457#117—734no—
458#117—734no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4C4×D7311yescharacteristic
473C2×C4⋊C4C4×D7311yescharacteristic
474C2×C4⋊C4C4×D7311yescharacteristic
475C2×C22⋊C4—731no—
476C2×C22⋊C4—731no—
477C2×C22⋊C4—731no—
478C2×C22⋊C4—731no—
479C2×C42—731no—
480C2×C42—731no—
481C2×C42—731no—
482C2×C42—731no—
483C2×C42—731no—
484C2×C42—734no—
485C2×C42—734no—
486C2×C42C22×D7311yescharacteristic
487C2×C42C22×D7311yescharacteristic
488C2×C42C22×D7311yescharacteristic
489C4⋊C8—734no—
490C4⋊C8—734no—
491C4⋊C8—734no—
492C4⋊C8—734no—
493C4⋊C8—734no—
494C4⋊C8—734no—
495C4⋊C8—734no—
496C4⋊C8—734no—
497C4⋊C8—734no—
498C4⋊C8C22×D7314yes—
499C4⋊C8C22×D7314yes—
500C4⋊C8C22×D7314yes—
501#97—734no—
502#97—734no—
503#97—734no—
504#97—734no—
505#97C22×D7314yes—
506#97C22×D7314yes—
507C4×C8—734no—
508C4×C8—734no—
509C4×C8—734no—
510C4×C8—734no—
511C4×C8—734no—
512C4×C8C22×D7314yes—
513C24—731no—
514C2×Q8—42no—
515C2×Q8—2922no—
516C2×Q8—734no—
517C2×Q8—734no—
518C2×Q8—734no—
519C2×Q8—1464no—
520C2×Q8—1464no—
521C2×Q8C2×C4×D7314yes—
522C22×C4—2922no—
523C22×C4—734no—
524C22×C4—731no—
525C22×C4—731no—
526C22×C4—732no—
527C22×C4—734no—
528C22×C4—734no—
529C22×C4—732no—
530C22×C4—731no—
531C22×C4—731no—
532C22×C4—731no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—734no—
536C22×C4—1464no—
537C22×C4C2×C4×D7311yescharacteristic
538C22×C4C2×C4×D7311yescharacteristic
539C22×C4C2×C4×D7311yescharacteristic
540C22×C4C2×C4×D7311yescharacteristic
541C22×C4C2×C4×D7311yescharacteristic
542C22×C4C2×C4×D7311yescharacteristic
543C22×C4C23×D7311yescharacteristic
544M16—7316no—
545M16—1468no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—734no—
550C2×C8—732no—
551C2×C8—732no—
552C2×C8—732no—
553C2×C8—732no—
554C2×C8—1468no—
555C2×C8—1468no—
556C2×C8—1462no—
557C2×C8—1462no—
558C2×C8—1462no—
559C2×C8Q8×D7314yes—
560C2×C8C23×D7312yes—
561C2×C8C23×D7312yes—
562C2×C8C23×D7312yes—
563C2×C8C23×D7312yes—
564C4⋊C4—734no—
565C4⋊C4—734no—
566C4⋊C4—734no—
567C4⋊C4—734no—
568C4⋊C4—734no—
569C4⋊C4—734no—
570C4⋊C4—734no—
571C4⋊C4—734no—
572C4⋊C4—734no—
573C4⋊C4—734no—
574C4⋊C4—734no—
575C4⋊C4—734no—
576C4⋊C4—734no—
577C4⋊C4C2×C4×D7314yes—
578C4⋊C4C2×C4×D7314yes—
579C4⋊C4C2×C4×D7314yes—
580C22⋊C4—734no—
581C22⋊C4—734no—
582C22⋊C4—734no—
583C22⋊C4—734no—
584C42—732no—
585C42—734no—
586C42—734no—
587C42—732no—
588C42—732no—
589C42—732no—
590C42—732no—
591C42—732no—
592C42C2×C4×D7312yes—
593C42C2×C4×D7312yes—
594C42C2×C4×D7312yes—
595C42C23×D7312yes—
596C42C23×D7312yes—
597C42C23×D7312yes—
598C23—732no—
599C23—734no—
600C23—1462no—
601C23—1462no—
602C23C22×C4×D7311yescharacteristic
603Q8—44no—
604Q8—2924no—
605Q8—1468no—
606Q8—1468no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—2924no—
614C2×C4—732no—
615C2×C4—732no—
616C2×C4—734no—
617C2×C4—734no—
618C2×C4—734no—
619C2×C4—734no—
620C2×C4—738no—
621C2×C4—732no—
622C2×C4—732no—
623C2×C4—732no—
624C2×C4—732no—
625C2×C4—732no—
626C2×C4—1468no—
627C2×C4—1462no—
628C2×C4—1462no—
629C2×C4—1462no—
630C2×C4—1462no—
631C2×C4—1462no—
632C2×C4C22×C4×D7312yes—
633C2×C4C22×C4×D7312yes—
634C2×C4C22×C4×D7312yes—
635C2×C4C22×C4×D7312yes—
636C2×C4C22×C4×D7312yes—
637C2×C4C22×C4×D7312yes—
638C2×C4C22×C4×D7311yescharacteristic
639C2×C4C2×Q8×D7312yes—
640C2×C4#41×D7312yes—
641C2×C4C24×D7311yescharacteristic
642C8—22no—
643C8—22no—
644C8—22no—
645C8—734no—
646C8—1462no—
647C8—1462no—
648C8—1462no—
649C8C2×Q8×D7314yes—
650C22—734no—
651C22—1462no—
652C22—1462no—
653C22—1468no—
654C22C4×Q8×D7312yes—
655C22#131×D7312yes—
656C22#1798935312yes—
657C22C23×C4×D7311yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—734no—
665C4—734no—
666C4—1462no—
667C4—1462no—
668C4—1462no—
669C4—1462no—
670C4—1462no—
671C4C4×Q8×D7312yes—
672C4C22×Q8×D7311yescharacteristic
673C4C2×#41×D7311yescharacteristic
674C2—1464no—
675C2#2261887614yesdirect product factor
676C2C2×C4×Q8×D7311yescharacteristic
677C2C2×#131×D7311yescharacteristic
678C2C2×#1798935311yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC2×C4C24×D73
FittingC2×#446×C73C2
socleC23×C73C23×C4
prime radicalC23×D73C22×C4
cosocleC2×C4×C73C25
hypercenterC2×#446D73
hypocenterC73C2×#2962
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #22618876C2direct (N × H)
3. C2×#17988718C2semidirect
4. C2×#17988716C2semidirect
5. C2×#17988716C2semidirect
6. C2×#17988715C2semidirect
7. C2×#17988715C2semidirect
8. C2×C8×Dic146C2semidirect
9. C2×#17988711C2semidirect
16. C2×#446×C73C2semidirect
37. #17988718C22semidirect
38. #17988716C22semidirect
39. #17988716C22semidirect
40. #17988715C22semidirect
41. #17988715C22semidirect
42. C8×Dic146C22semidirect
43. #17988711C22semidirect
69. #446×C73C22semidirect
83. C2×#11924011Q8semidirect
196. #11924011C2×Q8semidirect
335. C2×C73#2962semidirect
347. C2×#446D73semidirect
356. C73C2×#2962semidirect
383. #446C2×D73semidirect
675. C2#22618876direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891412
#226188762
C2×#179887182
C2×#179887162
C2×#179887152
C2×C8×Dic1462
C2×#179887112
C2×#179886122
C2×C4⋊C8×D732
C2×#179885442
C2×#179885412
C2×#179885392
C2×#446×C732
C2×#296273