Finite Group Databasebeta

← C2×#22623754 #33994464

Subgroups — C2×#22623754 #33994464

Order 18688.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623754C2132yesmaximal, direct product factor
2C2×#17989314C212yesmaximal, complemented
3C2×#17989312C212yesmaximal, complemented
4C2×#17989298C212yesmaximal, complemented
5C2×#17989295C214yesmaximal, complemented
6C2×#17989293C212yesmaximal, complemented
7C2×#17989291C214yesmaximal, complemented
8C2×#17989217C212yesmaximal, complemented
9C2×#17989215C211yesmaximal, characteristic, complemented
10C2×#17989214C212yesmaximal, complemented
11C2×#17989142C212yesmaximal, complemented
12C2×#17989140C211yesmaximal, characteristic, complemented
13C22×#14556582C211yesmaximal, characteristic, complemented
14C2×#125×D73C212yesmaximal, complemented
15C2×#17989068C211yesmaximal, characteristic
16C2×#17989067C211yesmaximal, characteristic
17C2×#17989055C211yesmaximal, characteristic
18C2×#544×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2211yescharacteristic
20#17989314C22132yescomplemented
21#17989312C22132yescomplemented
22#17989298C22132yescomplemented
23#17989295C22164yescomplemented
24#17989293C22132yescomplemented
25#17989291C22164yescomplemented
26#17989217C22132yescomplemented
27#17989215C22116yescomplemented
28#17989214C22132yescomplemented
29#17989142C22132yescomplemented
30#17989140C22116yescomplemented
31C2×#14556591C2212yes—
32C2×#14556590C2212yes—
33C2×#14556590C2214yes—
34C2×#14556590C2211yescharacteristic
35C2×#14556590C2211yescharacteristic
36C2×#14556589C2214yes—
37C2×#14556583C2212yes—
38C2×#14556582C2212yes—
39C2×#14556582C2212yes—
40C2×#14556582C2212yes—
41C2×#14556582C2212yes—
42C2×#14556582C2211yescharacteristic
43C2×#14556582C2212yes—
44C2×#14556582C2211yescharacteristic
45C2×#14556582C22116yescomplemented
46C2×#14556581C2214yes—
47C2×#14556581C2214yes—
48C2×#14556581C2214yes—
49C2×#14556581C2214yes—
50#125×D73C22132yescomplemented
51C2×#14556571C2214yes—
52C2×#14556571C2214yes—
53C2×#14556569C2214yes—
54C2×#14556569C2214yes—
55C2×#14556568C2214yes—
56C2×#14556568C2212yes—
57C2×#14556568C2212yes—
58C2×#14556567C2214yes—
59C2×#14556567C2214yes—
60#17989068C22116yes—
61#17989067C22116yes—
62#17989055C22116yes—
63C2×Q8×Dic73C2214yes—
64C2×C4×Dic146C2212yes—
65C2×C4×Dic146C2212yes—
66C2×C4×Dic146C2212yes—
67C2×#14556556C2211yescharacteristic
68C2×#14556556C2212yes—
69C2×#14556556C2211yescharacteristic
70C2×#14556556C2214yes—
71C2×C4×D292C2212yes—
72C2×#14556553C2211yescharacteristic
73C2×#14556553C2211yescharacteristic
74C2×#14556553C2212yes—
75C2×C4×C22⋊D73C2214yes—
76C2×#14556551C2212yes—
77C2×#14556551C2212yes—
78C2×#14556551C2214yes—
79C2×#14556550C2211yescharacteristic
80C2×#14556549C2212yes—
81C2×#14556549C2212yes—
82C2×#14556548C2212yes—
83C22×C4⋊Dic73C2211yescharacteristic
84C22×C4⋊Dic73C2212yes—
85C22×#11924007C2212yes—
86C2×C4⋊C4×D73C2212yes—
87C2×C4⋊C4×D73C2212yes—
88C2×C4⋊C4×D73C2214yes—
89C2×C4⋊C4×D73C2214yes—
90C22×C4×Dic73C2211yescharacteristic
91C2×C42×D73C2212yes—
92#544×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2212yes—
94C2×C4⋊Q8×C73C2212yes—
95C2×#125×C73C2212yes—
96C2×#125×C73C2212yes—
97C2×C22⋊Q8×C73C2214yes—
98C2×#117×C73C2211yescharacteristic
99C2×#117×C73C2211yescharacteristic
100C22×C4⋊C4×C73C2211yescharacteristic
101C2×#11924028Q8116yescomplemented
102C2×#11924028C2318yes—
103C22×Dic146C2312yes—
104C22×Dic146C2312yes—
105C22×Dic146C2314yes—
106C22×Dic146C2311yescharacteristic
107C22×D292C2311yescharacteristic
108C22×C22⋊D73C2312yes—
109C23×Dic73C2311yescharacteristic
110C23×Dic73C2311yescharacteristic
111C23×Dic73C2312yes—
112C22×C4×D73C2312yes—
113C22×C4×D73C2312yes—
114C22×C4×D73C2314yes—
115C22×C4×D73C2314yes—
116C22×C4×D73C2312yes—
117#14556591C23116yes—
118#14556590C2318yes—
119#14556590C2318yes—
120#14556590C23116yes—
121#14556590C23132yes—
122#14556589C23132yes—
123#14556583C23116yes—
124#14556582C2318yes—
125#14556582C2318yes—
126#14556582C23116yes—
127#14556582C23116yes—
128#14556582C23116yes—
129#14556582C23116yes—
130#14556582C23116yes—
131#14556581C23132yes—
132#14556581C23132yes—
133#14556581C23132yes—
134#14556581C23132yes—
135#14556571C23132yes—
136#14556571C23132yes—
137#14556569C23132yes—
138#14556569C23132yes—
139#14556568C23116yes—
140#14556568C23116yes—
141#14556568C23132yes—
142#14556567C23132yes—
143#14556567C23132yes—
144Q8×Dic73C23132yes—
145C4×Dic146C23116yes—
146C4×Dic146C23116yes—
147C4×Dic146C23116yes—
148#14556556C23132yes—
149#14556556C2318yes—
150#14556556C2318yes—
151#14556556C23116yes—
152C4×D292C23116yes—
153#14556553C2318yes—
154#14556553C23116yes—
155#14556553C2318yes—
156C4×C22⋊D73C23132yes—
157#14556551C23116yes—
158#14556551C23132yes—
159#14556551C23116yes—
160#14556550C2318yes—
161#14556549C23116yes—
162#14556549C23116yes—
163#14556548C23116yes—
164C2×C4⋊Dic73C2311yescharacteristic
165C2×C4⋊Dic73C2311yescharacteristic
166C2×C4⋊Dic73C2312yes—
167C2×C4⋊Dic73C2314yes—
168C2×C4⋊Dic73C2312yes—
169C2×C4⋊Dic73C2314yes—
170C2×C4⋊Dic73C2318yes—
171C2×C4⋊Dic73C2312yes—
172C2×C4⋊Dic73C2314yes—
173C2×C4⋊Dic73C23116yes—
174C2×C4⋊Dic73C2312yes—
175C2×#11924007C2312yes—
176C2×#11924007C2314yes—
177C2×#11924007C2314yes—
178C2×#11924007C2314yes—
179C2×#11924007C2312yes—
180C2×#11924007C2314yes—
181C2×#11924007C2314yes—
182C2×#11924007C2312yes—
183C2×#11924007C2312yes—
184C2×#11924007C23116yes—
185C2×#11924007C2312yes—
186C2×#11924007C2314yes—
187C2×#11924007C2312yes—
188C4⋊C4×D73C23116yes—
189C4⋊C4×D73C23116yes—
190C4⋊C4×D73C23132yes—
191C4⋊C4×D73C23132yes—
192C2×C22⋊Dic73C2312yes—
193C2×#11924005C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2314yes—
196C2×#11924005C2314yes—
197C2×C4×Dic73C2314yes—
198C2×C4×Dic73C2311yescharacteristic
199C2×C4×Dic73C2314yes—
200C2×C4×Dic73C2312yes—
201C2×C4×Dic73C2318yes—
202C2×C4×Dic73C2311yescharacteristic
203C2×C4×Dic73C2312yes—
204C2×C4×Dic73C2312yes—
205C2×C4×Dic73C2311yescharacteristic
206C2×C4×Dic73C2311yescharacteristic
207C42×D73C23116yes—
208C22×Q8×C73C2314yes—
209C23×C4×C73C2312yes—
210C23×C4×C73C2311yescharacteristic
211C4⋊Q8×C73C23116yes—
212C4⋊Q8×C73C23116yes—
213#125×C73C23116yes—
214#125×C73C23116yes—
215C22⋊Q8×C73C23132yes—
216#117×C73C2318yes—
217#117×C73C2318yes—
218C2×C4⋊C4×C73C2311yescharacteristic
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2314yes—
222C2×C4⋊C4×C73C2312yes—
223C2×C4⋊C4×C73C2312yes—
224C2×C4⋊C4×C73C2318yes—
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2314yes—
227C2×C4⋊C4×C73C2314yes—
228C2×C22⋊C4×C73C2312yes—
229C2×C22⋊C4×C73C2312yes—
230C2×C42×C73C2312yes—
231C2×C42×C73C2312yes—
232C23×D73C2412yes—
233#11924028C2×Q8164yescomplemented
234C2×Dic146—44no—
235C2×Dic146—48no—
236C2×Dic146—44no—
237C2×Dic146C2×Q818yes—
238C2×Dic146C24116yes—
239C2×Dic146C2418yes—
240C2×Dic146C2418yes—
241C2×Dic146C2414yes—
242C2×D292C2×Q818yes—
243C2×D292C2414yes—
244C2×C22⋊D73C2×Q8116yes—
245C2×C22⋊D73C2418yes—
246C22×Dic73—42no—
247C22×Dic73—42no—
248C22×Dic73—44no—
249C22×Dic73C2411yescharacteristic
250C22×Dic73C2411yescharacteristic
251C22×Dic73C2412yes—
252C22×Dic73C2411yescharacteristic
253C22×Dic73C2411yescharacteristic
254C22×Dic73C2414yes—
255C22×Dic73C2412yes—
256C22×Dic73C2414yes—
257C22×Dic73C2414yes—
258C22×Dic73C2418yes—
259C22×Dic73C2412yes—
260C2×C4×D73—44no—
261C2×C4×D73—44no—
262C2×C4×D73—48no—
263C2×C4×D73—48no—
264C2×C4×D73C2×Q8116yes—
265C2×C4×D73C2418yes—
266C2×C4×D73C2418yes—
267C2×C4×D73C24116yes—
268C2×C4×D73C24116yes—
269C2×C4×D73C2418yes—
270C4⋊Dic73C2414yes—
271C4⋊Dic73C2418yes—
272C4⋊Dic73C2418yes—
273C4⋊Dic73C24116yes—
274C4⋊Dic73C2418yes—
275C4⋊Dic73C24116yes—
276C4⋊Dic73C2414yes—
277C4⋊Dic73C2418yes—
278C4⋊Dic73C24116yes—
279#11924007C2418yes—
280#11924007C24116yes—
281#11924007C24116yes—
282#11924007C24116yes—
283#11924007C24116yes—
284#11924007C24116yes—
285#11924007C24116yes—
286#11924007C2418yes—
287#11924007C2418yes—
288#11924007C2418yes—
289#11924007C2418yes—
290#11924007C2418yes—
291C22⋊Dic73C2418yes—
292#11924005C2418yes—
293#11924005C2418yes—
294#11924005C24116yes—
295#11924005C24116yes—
296C4×Dic73C2414yes—
297C4×Dic73C2418yes—
298C4×Dic73C2418yes—
299C4×Dic73C2414yes—
300C4×Dic73C2414yes—
301C4×Dic73C2414yes—
302C4×Dic73C24116yes—
303C4×Dic73C24116yes—
304C4×Dic73C2418yes—
305C24×C73C2411yescharacteristic
306C2×Q8×C73—48no—
307C2×Q8×C73C24116yes—
308C22×C4×C73—44no—
309C22×C4×C73C2×Q818yes—
310C22×C4×C73C2412yes—
311C22×C4×C73C2412yes—
312C22×C4×C73C2412yes—
313C22×C4×C73C2412yes—
314C22×C4×C73C2414yes—
315C22×C4×C73C2418yes—
316C22×C4×C73C2411yescharacteristic
317C22×C4×C73C2411yescharacteristic
318C22×C4×C73C2414yes—
319C4⋊C4×C73C2418yes—
320C4⋊C4×C73C2418yes—
321C4⋊C4×C73C2414yes—
322C4⋊C4×C73C2414yes—
323C4⋊C4×C73C2414yes—
324C4⋊C4×C73C2414yes—
325C4⋊C4×C73C24116yes—
326C4⋊C4×C73C24116yes—
327C4⋊C4×C73C24116yes—
328C22⋊C4×C73C2418yes—
329C22⋊C4×C73C2418yes—
330C42×C73C2418yes—
331C42×C73C2418yes—
332C23×C73—22no—
333C23×C73—22no—
334C23×C73C22×Q814yes—
335C23×C73C2512yes—
336C23×C73C2511yescharacteristic
337C22×D73—24no—
338C22×D73—24no—
339C22×D73C22×Q818yes—
340C22×D73C2514yes—
341Q8×C73—416no—
342C2×C4×C73—28no—
343C2×C4×C73—24no—
344C2×C4×C73—24no—
345C2×C4×C73—24no—
346C2×C4×C73—24no—
347C2×C4×C73—48no—
348C2×C4×C73C22×Q814yes—
349C2×C4×C73C22×Q814yes—
350C2×C4×C73C22×Q8116yes—
351C2×C4×C73C2514yes—
352C2×C4×C73C2514yes—
353C2×C4×C73C2514yes—
354C2×C4×C73C2514yes—
355C2×C4×C73C2518yes—
356C2×C4×C73C2512yes—
357C2×C4×C73C2512yes—
358C22⋊D73C22×Q8132yes—
359C2×Dic73—22no—
360C2×Dic73—22no—
361C2×Dic73—24no—
362C2×Dic73—28no—
363C2×Dic73—22no—
364C2×Dic73—22no—
365C2×Dic73—24no—
366C2×Dic73—44no—
367C2×Dic73—44no—
368C2×Dic73—48no—
369C2×Dic73C22×Q818yes—
370C2×Dic73C2512yes—
371C2×Dic73C2512yes—
372C2×Dic73C2514yes—
373C2×Dic73C2512yes—
374C2×Dic73C2512yes—
375C2×Dic73C2518yes—
376C2×Dic73C2514yes—
377C2×Dic73C2514yes—
378D292C22×Q8116yes—
379C4×D73—416no—
380C4×D73—416no—
381C4×D73—48no—
382C4×D73—48no—
383C4×D73C22×Q8132yes—
384Dic146—48no—
385Dic146—416no—
386Dic146—48no—
387Dic146C22×Q8116yes—
388C22×C73—22no—
389C22×C73—22no—
390C22×C73—28no—
391C22×C73C23×Q814yes—
392C22×C73C23×Q812yes—
393C22×C73#58512yes—
394C22×C73#58512yes—
395C22×C73C2611yescharacteristic
396C2×D73—24no—
397C2×D73—24no—
398C2×D73—216no—
399C2×D73C23×Q818yes—
400C4×C73—24no—
401C4×C73—24no—
402C4×C73—24no—
403C4×C73—28no—
404C4×C73—24no—
405C4×C73C23×Q814yes—
406C4×C73C23×Q814yes—
407Dic73—24no—
408Dic73—22no—
409Dic73—22no—
410Dic73—24no—
411Dic73—28no—
412Dic73—22no—
413Dic73—22no—
414Dic73C23×Q818yes—
415C2×#3504—731nomaximal, Sylow
416C2×C73—24no—
417C2×C73#350414yescomplemented
418C2×C73C24×Q811yescharacteristic
419C2×C73C2×#58511yescharacteristic
420C2×C73C2×#58511yescharacteristic
421D73—28no—
422#3504—7332no—
423C2×#557—732no—
424C2×#557—732no—
425C2×#554—732no—
426C2×#554—732no—
427C2×#554—734no—
428C2×#554—734no—
429C2×#544—732no—
430C2×#544—732no—
431C2×#544—731no—
432C2×#544D7311yescharacteristic, complemented
433C2×#533—732no—
434C2×#533—731no—
435C22×#125—732no—
436C22×#125—731no—
437C2×#520—731no—
438C2×#520—731no—
439C2×C4×#41—731no—
440C73C2×#350411yescharacteristic, complemented, Sylow
441C22×#41—731no—
442#557—7332no—
443#557—7332no—
444#554—7332no—
445#554—7332no—
446#554—7364no—
447#554—7364no—
448#544—7332no—
449#544—7332no—
450#544—7316no—
451#544C2×D73116yescomplemented
452#533—7332no—
453#533—7316no—
454C2×C4⋊Q8—734no—
455C2×C4⋊Q8—731no—
456C2×C4⋊Q8—731no—
457C2×C4⋊Q8—734no—
458C2×C4⋊Q8—732no—
459C2×C4⋊Q8—732no—
460C2×C4⋊Q8C2×D7312yes—
461C2×C4⋊Q8C2×D7312yes—
462C2×#125—7332no—
463C2×#125—731no—
464C2×#125—732no—
465C2×#125—732no—
466C2×#125—734no—
467C2×#125—734no—
468C2×#125—732no—
469C2×#125—732no—
470C2×#125—7316no—
471C2×#125—731no—
472C2×#125—734no—
473C2×#125—734no—
474C2×#125—732no—
475C2×#125—732no—
476C2×#125C2×D7312yes—
477C2×#125C2×D7312yes—
478C2×C22⋊Q8—734no—
479C2×C22⋊Q8—734no—
480C2×C22⋊Q8—734no—
481C2×C22⋊Q8—734no—
482C2×C22⋊Q8—734no—
483C2×C22⋊Q8—734no—
484C2×C22⋊Q8—732no—
485C2×C22⋊Q8—732no—
486C2×C22⋊Q8—734no—
487C2×C22⋊Q8C2×D7314yes—
488#520—7316no—
489#520—7316no—
490C4×#41—7316no—
491C2×C4×Q8—734no—
492C2×C4×Q8—731no—
493C2×C4×Q8—731no—
494C2×C4×Q8—732no—
495C2×C4×Q8—734no—
496C2×C4×Q8—732no—
497C2×C4×Q8—732no—
498C2×C4×Q8—732no—
499C2×C4×D4—734no—
500C2×C4×D4—731no—
501C2×C4×D4—731no—
502C2×C4×D4—732no—
503C2×C4×D4—732no—
504C2×C4×D4—732no—
505C2×C4×D4—734no—
506C2×C4×D4—732no—
507C2×#117—731no—
508C2×#117—732no—
509C2×#117—732no—
510C2×#117—732no—
511C2×#117C2×D7311yescharacteristic
512C2×#117C2×D7311yescharacteristic
513C22×C4⋊C4—731no—
514C22×C4⋊C4—732no—
515C22×C4⋊C4—732no—
516C22×C4⋊C4—732no—
517C22×C4⋊C4—732no—
518C22×C4⋊C4—734no—
519C22×C4⋊C4—734no—
520C22×C4⋊C4C2×D7311yescharacteristic
521C22×C42—731no—
522C22×C42—732no—
523C2×#41—7316no—
524C2×#41—738no—
525C22×Q8—732no—
526C22×Q8—734no—
527C22×Q8—732no—
528C22×Q8—731no—
529C22×Q8C22×D7314yes—
530C22×D4—732no—
531C22×D4—731no—
532C23×C4—732no—
533C23×C4—731no—
534C23×C4—731no—
535C23×C4—734no—
536C23×C4—734no—
537C23×C4—732no—
538C23×C4—732no—
539C23×C4—732no—
540C23×C4C22×D7312yes—
541C23×C4C22×D7311yescharacteristic
542C4⋊Q8—7332no—
543C4⋊Q8—738no—
544C4⋊Q8—738no—
545C4⋊Q8—7332no—
546C4⋊Q8—7316no—
547C4⋊Q8—7316no—
548C4⋊Q8C22×D73116yes—
549C4⋊Q8C22×D73116yes—
550#125—738no—
551#125—7316no—
552#125—7316no—
553#125—7332no—
554#125—7332no—
555#125—7316no—
556#125—7316no—
557#125—738no—
558#125—7332no—
559#125—7332no—
560#125—7316no—
561#125—7316no—
562#125C22×D73116yes—
563#125C22×D73116yes—
564C22⋊Q8—7332no—
565C22⋊Q8—7332no—
566C22⋊Q8—7332no—
567C22⋊Q8—7332no—
568C22⋊Q8—7332no—
569C22⋊Q8—7332no—
570C22⋊Q8—7316no—
571C22⋊Q8—7316no—
572C22⋊Q8—7332no—
573C22⋊Q8C22×D73132yes—
574C4×Q8—7332no—
575C4×Q8—738no—
576C4×Q8—738no—
577C4×Q8—7316no—
578C4×Q8—7332no—
579C4×Q8—7316no—
580C4×Q8—7316no—
581C4×Q8—7316no—
582C4×D4—7332no—
583C4×D4—738no—
584C4×D4—738no—
585C4×D4—7316no—
586C4×D4—7316no—
587C4×D4—7316no—
588C4×D4—7332no—
589C4×D4—7316no—
590#117—738no—
591#117—7316no—
592#117—7316no—
593#117—7316no—
594#117C22×D7318yes—
595#117C22×D7318yes—
596C2×C4⋊C4—732no—
597C2×C4⋊C4—731no—
598C2×C4⋊C4—734no—
599C2×C4⋊C4—732no—
600C2×C4⋊C4—734no—
601C2×C4⋊C4—732no—
602C2×C4⋊C4—734no—
603C2×C4⋊C4—734no—
604C2×C4⋊C4—732no—
605C2×C4⋊C4—738no—
606C2×C4⋊C4—734no—
607C2×C4⋊C4—734no—
608C2×C4⋊C4—734no—
609C2×C4⋊C4—734no—
610C2×C4⋊C4—7316no—
611C2×C4⋊C4—7316no—
612C2×C4⋊C4—731no—
613C2×C4⋊C4—732no—
614C2×C4⋊C4—732no—
615C2×C4⋊C4—732no—
616C2×C4⋊C4—732no—
617C2×C4⋊C4—732no—
618C2×C4⋊C4—732no—
619C2×C4⋊C4—734no—
620C2×C4⋊C4—7316no—
621C2×C4⋊C4—7316no—
622C2×C4⋊C4—7332no—
623C2×C4⋊C4—7332no—
624C2×C4⋊C4C22×D7311yescharacteristic
625C2×C4⋊C4C22×D7312yes—
626C2×C4⋊C4C22×D7314yes—
627C2×C4⋊C4C22×D7314yes—
628C2×C4⋊C4C22×D7312yes—
629C2×C4⋊C4C22×D7318yes—
630C2×C4⋊C4C22×D7311yescharacteristic
631C2×C4⋊C4C22×D7311yescharacteristic
632C2×C4⋊C4C22×D7311yescharacteristic
633C2×C4⋊C4C22×D7314yes—
634C2×C22⋊C4—732no—
635C2×C22⋊C4—734no—
636C2×C22⋊C4—732no—
637C2×C22⋊C4—732no—
638C2×C22⋊C4—734no—
639C2×C22⋊C4C22×D7312yes—
640C2×C22⋊C4C22×D7312yes—
641C2×C42—731no—
642C2×C42—734no—
643C2×C42—734no—
644C2×C42—732no—
645C2×C42—732no—
646C2×C42—732no—
647C2×C42—731no—
648C2×C42—731no—
649C2×C42—738no—
650C2×C42—731no—
651C2×C42—7316no—
652C2×C42C22×D7312yes—
653C2×C42C22×D7312yes—
654C24—732no—
655C24C23×D7311yescharacteristic
656#41—7364no—
657C2×Q8—48no—
658C2×Q8—2924no—
659C2×Q8—2924no—
660C2×Q8—2928no—
661C2×Q8—738no—
662C2×Q8—738no—
663C2×Q8—7316no—
664C2×Q8—738no—
665C2×Q8—734no—
666C2×Q8C23×D73116yes—
667C2×D4—7316no—
668C2×D4—738no—
669C2×D4—738no—
670C2×D4—734no—
671C22×C4—44no—
672C22×C4—2928no—
673C22×C4—2924no—
674C22×C4—2928no—
675C22×C4—2924no—
676C22×C4—2922no—
677C22×C4—2922no—
678C22×C4—2924no—
679C22×C4—734no—
680C22×C4—734no—
681C22×C4—738no—
682C22×C4—738no—
683C22×C4—738no—
684C22×C4—7316no—
685C22×C4—7316no—
686C22×C4—732no—
687C22×C4—7316no—
688C22×C4—738no—
689C22×C4—731no—
690C22×C4—731no—
691C22×C4—732no—
692C22×C4—731no—
693C22×C4—731no—
694C22×C4—732no—
695C22×C4—734no—
696C22×C4Q8×D7318yes—
697C22×C4C23×D7312yes—
698C22×C4C23×D7312yes—
699C22×C4C23×D7312yes—
700C22×C4C23×D7314yes—
701C22×C4C23×D7312yes—
702C22×C4C23×D7318yes—
703C22×C4C23×D7314yes—
704C22×C4C23×D7311yescharacteristic
705C22×C4C23×D7311yescharacteristic
706C4⋊C4—7316no—
707C4⋊C4—738no—
708C4⋊C4—7316no—
709C4⋊C4—7316no—
710C4⋊C4—7316no—
711C4⋊C4—7316no—
712C4⋊C4—7316no—
713C4⋊C4—738no—
714C4⋊C4—738no—
715C4⋊C4—738no—
716C4⋊C4—738no—
717C4⋊C4—738no—
718C4⋊C4—734no—
719C4⋊C4—738no—
720C4⋊C4—7316no—
721C4⋊C4—738no—
722C4⋊C4—738no—
723C4⋊C4—7316no—
724C4⋊C4—734no—
725C4⋊C4—738no—
726C4⋊C4—7316no—
727C4⋊C4C23×D7314yes—
728C4⋊C4C23×D7318yes—
729C4⋊C4C23×D73116yes—
730C4⋊C4C23×D73116yes—
731C4⋊C4C23×D7318yes—
732C4⋊C4C23×D7314yes—
733C4⋊C4C23×D7314yes—
734C4⋊C4C23×D7314yes—
735C4⋊C4C23×D73116yes—
736C22⋊C4—738no—
737C22⋊C4—7316no—
738C22⋊C4—738no—
739C22⋊C4—738no—
740C22⋊C4—7316no—
741C22⋊C4C23×D7318yes—
742C22⋊C4C23×D7318yes—
743C42—734no—
744C42—734no—
745C42—738no—
746C42—738no—
747C42—734no—
748C42—734no—
749C42—7316no—
750C42—7316no—
751C42—738no—
752C42C23×D7318yes—
753C42C23×D7318yes—
754C23—22no—
755C23—22no—
756C23—738no—
757C23—734no—
758C23—1464no—
759C23—1464no—
760C23C2×Q8×D7314yes—
761C23C24×D7312yes—
762C23C24×D7311yescharacteristic
763Q8—416no—
764Q8—2928no—
765Q8—2928no—
766Q8—29216no—
767Q8—7316no—
768D4—7332no—
769D4—7316no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—29216no—
777C2×C4—2928no—
778C2×C4—29216no—
779C2×C4—2928no—
780C2×C4—2924no—
781C2×C4—2924no—
782C2×C4—2928no—
783C2×C4—738no—
784C2×C4—734no—
785C2×C4—7332no—
786C2×C4—732no—
787C2×C4—732no—
788C2×C4—734no—
789C2×C4—732no—
790C2×C4—732no—
791C2×C4—734no—
792C2×C4—738no—
793C2×C4—1462no—
794C2×C4—1464no—
795C2×C4—1462no—
796C2×C4—1462no—
797C2×C4—1468no—
798C2×C4—1462no—
799C2×C4—1464no—
800C2×C4C2×Q8×D7314yes—
801C2×C4C2×Q8×D7314yes—
802C2×C4C2×Q8×D73116yes—
803C2×C4C24×D7314yes—
804C2×C4C24×D7314yes—
805C2×C4C24×D7314yes—
806C2×C4C24×D7318yes—
807C2×C4C24×D7314yes—
808C2×C4C24×D7312yes—
809C2×C4C24×D7312yes—
810C22—28no—
811C22—22no—
812C22—22no—
813C22—738no—
814C22—14616no—
815C22—1464no—
816C22—1464no—
817C22C22×Q8×D7314yes—
818C22C22×Q8×D7312yes—
819C22#1798942212yes—
820C22#1798942412yes—
821C22C25×D7311yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—738no—
828C4—1462no—
829C4—1464no—
830C4—1462no—
831C4—1462no—
832C4—1468no—
833C4—1462no—
834C4—1464no—
835C4C22×Q8×D7314yes—
836C4C22×Q8×D7314yes—
837C2—24no—
838C2—1468no—
839C2#2262375414yesdirect product factor
840C2C23×Q8×D7311yescharacteristic
841C2C2×#1798942211yescharacteristic
842C2C2×#1798942411yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#544×C73C2
socleC23×C73C25
prime radicalC22×#11924028C22
hypercenterC2×#544D73
hypocenterC73C2×#3504
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #22623754C2direct (N × H)
2. C2×#17989314C2semidirect
3. C2×#17989312C2semidirect
4. C2×#17989298C2semidirect
5. C2×#17989295C2semidirect
6. C2×#17989293C2semidirect
7. C2×#17989291C2semidirect
8. C2×#17989217C2semidirect
9. C2×#17989215C2semidirect
10. C2×#17989214C2semidirect
11. C2×#17989142C2semidirect
12. C2×#17989140C2semidirect
13. C22×#14556582C2semidirect
14. C2×#125×D73C2semidirect
18. C2×#544×C73C2semidirect
20. #17989314C22semidirect
21. #17989312C22semidirect
22. #17989298C22semidirect
23. #17989295C22semidirect
24. #17989293C22semidirect
25. #17989291C22semidirect
26. #17989217C22semidirect
27. #17989215C22semidirect
28. #17989214C22semidirect
29. #17989142C22semidirect
30. #17989140C22semidirect
45. C2×#14556582C22semidirect
50. #125×D73C22semidirect
92. #544×C73C22semidirect
101. C2×#11924028Q8semidirect
233. #11924028C2×Q8semidirect
417. C2×C73#3504semidirect
432. C2×#544D73semidirect
440. C73C2×#3504semidirect
451. #544C2×D73semidirect
839. C2#22623754direct (N × H)

Maximal subgroups

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

subgroupindex
#226237542
C2×#179893142
C2×#179893122
C2×#179892982
C2×#179892952
C2×#179892932
C2×#179892912
C2×#179892172
C2×#179892152
C2×#179892142
C2×#179891422
C2×#179891402
C22×#145565822
C2×#125×D732
C2×#179890682
C2×#179890672
C2×#179890552
C2×#544×C732
C2×#350473