Finite Group Databasebeta

← C2×#22623521 #33993038

Subgroups — C2×#22623521 #33993038

Order 18688.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623521C2132yesmaximal, direct product factor
2C2×#17989319C213yesmaximal, complemented
3C2×#17989313C211yesmaximal, characteristic, complemented
4C2×#17989308C213yesmaximal, complemented
5C2×#17989289C213yesmaximal, complemented
6C2×#17989283C213yesmaximal, complemented
7C2×#17989256C211yesmaximal, characteristic, complemented
8C2×#17989248C211yesmaximal, characteristic, complemented
9C2×#17989132C213yesmaximal, complemented
10C2×#17989123C213yesmaximal, complemented
11C2×#17989116C213yesmaximal, complemented
12C2×#41×Dic73C211yesmaximal, characteristic, complemented
13C2×C4×#11924029C211yesmaximal, characteristic, complemented
14C2×C4×#11924027C213yesmaximal, complemented
15C22×Q8×Dic73C211yesmaximal, characteristic, complemented
16C2×#548×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×#11924027C2213yes—
19#17989319C22148yescomplemented
20#17989313C22116yescomplemented
21#17989308C22148yescomplemented
22#17989289C22148yescomplemented
23#17989283C22148yescomplemented
24#17989256C22116yescomplemented
25#17989248C22116yescomplemented
26#17989132C22148yescomplemented
27C2×#14556590C2213yes—
28C2×#14556587C2213yes—
29#17989123C22148yescomplemented
30#17989116C22148yescomplemented
31C2×#14556586C2216yes—
32C2×#14556584C2216yes—
33C2×#14556583C2213yes—
34C2×#14556582C2213yes—
35C2×#14556580C2213yes—
36C2×#14556577C2216yes—
37C2×#14556575C2216yes—
38C2×#14556573C2216yes—
39C2×#14556567C2213yes—
40C2×#14556565C2213yes—
41C2×#14556565C2213yes—
42C2×#14556563C2216yes—
43C2×#14556562C2213yes—
44#41×Dic73C22116yescomplemented
45C4×#11924029C22116yescomplemented
46C4×#11924027C22148yescomplemented
47C2×Q8×Dic73C2211yescharacteristic
48C2×Q8×Dic73C2211yescharacteristic
49C2×Q8×Dic73C2213yes—
50C2×Q8×Dic73C2211yescharacteristic
51C2×Q8×Dic73C2213yes—
52C2×Q8×Dic73C22116yescomplemented
53C2×C4×Dic146C2213yes—
54C2×#14556556C2213yes—
55C2×C4×D292C2213yes—
56C2×D4×Dic73C2213yes—
57C2×D4×Dic73C2213yes—
58C2×D4×Dic73C2213yes—
59C2×#14556553C2213yes—
60C2×C4×C22⋊D73C2213yes—
61C2×C4×C22⋊D73C2213yes—
62C2×#14556551C2213yes—
63C2×#14556551C2213yes—
64C2×#14556551C2216yes—
65C2×#14556550C2213yes—
66C2×#14556549C2213yes—
67C2×#14556549C2213yes—
68C2×#14556547C2211yescharacteristic
69C2×#14556547C2213yes—
70C22×C4⋊Dic73C2213yes—
71C22×C4×Dic73C2213yes—
72C22×C4×Dic73C2213yes—
73C2×C42×D73C2213yes—
74C22×#41×C73C2211yescharacteristic
75C23×Q8×C73C2211yescharacteristic
76#548×C73C22116yescomplemented
77C2×#124×C73C2213yes—
78C2×C22⋊Q8×C73C2213yes—
79C2×#121×C73C2213yes—
80C2×C4×Q8×C73C2211yescharacteristic
81C2×C4×D4×C73C2213yes—
82C2×#11924029—28no—
83C2×#11924029C2318yes—
84C2×#11924027—224no—
85C2×#11924027C23124yes—
86C22×Dic146C2313yes—
87C22×D292C2313yes—
88C22×C22⋊D73C2313yes—
89C22×C22⋊D73C2313yes—
90C22×C22⋊D73C2316yes—
91C23×Dic73C2313yes—
92C23×Dic73C2313yes—
93C23×Dic73C2313yes—
94C23×Dic73C2311yescharacteristic
95C22×C4×D73C2313yes—
96C22×C4×D73C2313yes—
97C22×C4×D73C2313yes—
98#14556590C23124yes—
99#14556587C23124yes—
100#14556586C23148yes—
101#14556584C23148yes—
102#14556583C23124yes—
103#14556582C23124yes—
104#14556580C23124yes—
105#14556577C23148yes—
106#14556575C23148yes—
107#14556573C23148yes—
108#14556567C23124yes—
109#14556565C23124yes—
110#14556565C23124yes—
111#14556563C23148yes—
112#14556562C23124yes—
113Q8×Dic73C23124yes—
114Q8×Dic73C2318yes—
115Q8×Dic73C2318yes—
116Q8×Dic73C23124yes—
117Q8×Dic73C2318yes—
118C4×Dic146C23124yes—
119#14556556C23124yes—
120C4×D292C23124yes—
121D4×Dic73C23124yes—
122D4×Dic73C23124yes—
123D4×Dic73C23124yes—
124#14556553C23124yes—
125C4×C22⋊D73C23124yes—
126C4×C22⋊D73C23124yes—
127#14556551C23148yes—
128#14556551C23124yes—
129#14556551C23124yes—
130#14556550C23124yes—
131#14556549C23124yes—
132#14556549C23124yes—
133#14556547C2318yes—
134#14556547C23124yes—
135C2×C4⋊Dic73C2313yes—
136C2×C4⋊Dic73C23124yes—
137C2×C4⋊Dic73C2313yes—
138C2×C4⋊Dic73C2313yes—
139C2×C4⋊Dic73C2316yes—
140C2×C4⋊Dic73C2313yes—
141C2×#11924007C2316yes—
142C2×#11924007C2311yescharacteristic
143C2×#11924007C2313yes—
144C2×#11924007C2311yescharacteristic
145C2×#11924007C2313yes—
146C2×C22⋊Dic73C2311yescharacteristic
147C2×C22⋊Dic73C2313yes—
148C2×C22⋊Dic73C2316yes—
149C2×#11924005C2313yes—
150C2×#11924005C2313yes—
151C2×#11924005C2316yes—
152C2×#11924005C2316yes—
153C2×C4×Dic73C23124yes—
154C2×C4×Dic73C2313yes—
155C2×C4×Dic73C23124yes—
156C2×C4×Dic73C2311yescharacteristic
157C2×C4×Dic73C2313yes—
158C2×C4×Dic73C2313yes—
159C2×C4×Dic73C2311yescharacteristic
160C2×C4×Dic73C2313yes—
161C2×C4×Dic73C2313yes—
162C2×C4×Dic73C2313yes—
163C2×C4×Dic73C2313yes—
164C42×D73C23124yes—
165C2×#41×C73—28no—
166C2×#41×C73C2318yes—
167C22×Q8×C73—28no—
168C22×Q8×C73C2318yes—
169C22×Q8×C73C2313yes—
170C22×Q8×C73C2311yescharacteristic
171C22×D4×C73C2313yes—
172C22×D4×C73C2313yes—
173C23×C4×C73C2313yes—
174C23×C4×C73C2313yes—
175#124×C73C23124yes—
176C22⋊Q8×C73C23124yes—
177#121×C73C23124yes—
178C4×Q8×C73C2318yes—
179C4×D4×C73C23124yes—
180C2×C4⋊C4×C73C2313yes—
181C2×C4⋊C4×C73C2313yes—
182C2×C22⋊C4×C73C2311yescharacteristic
183C2×C22⋊C4×C73C2313yes—
184C2×C22⋊C4×C73C2316yes—
185C2×C42×C73C2313yes—
186C23×D73C2413yes—
187#11924029—232no—
188#11924027—296no—
189C2×Dic146—212no—
190C2×Dic146C24112yes—
191C2×D292—212no—
192C2×D292C24112yes—
193C2×C22⋊D73—212no—
194C2×C22⋊D73—212no—
195C2×C22⋊D73—412no—
196C2×C22⋊D73C24112yes—
197C2×C22⋊D73C24112yes—
198C2×C22⋊D73C24124yes—
199C22×Dic73—212no—
200C22×Dic73—46no—
201C22×Dic73—46no—
202C22×Dic73#4118yescomplemented
203C22×Dic73C2411yescharacteristic
204C22×Dic73C2413yes—
205C22×Dic73C2411yescharacteristic
206C22×Dic73C2413yes—
207C22×Dic73C2413yes—
208C22×Dic73C24112yes—
209C22×Dic73C24112yes—
210C22×Dic73C24112yes—
211C22×Dic73C2411yescharacteristic
212C22×Dic73C2411yescharacteristic
213C22×Dic73C2414yes—
214C2×C4×D73—212no—
215C2×C4×D73—212no—
216C2×C4×D73—46no—
217C2×C4×D73C24112yes—
218C2×C4×D73C24112yes—
219C2×C4×D73C24112yes—
220C4⋊Dic73C24112yes—
221C4⋊Dic73C24112yes—
222C4⋊Dic73C24124yes—
223C4⋊Dic73C24112yes—
224C4⋊Dic73C24112yes—
225#11924007C2414yes—
226#11924007C24112yes—
227#11924007C2414yes—
228#11924007C24112yes—
229#11924007C24124yes—
230C22⋊Dic73C2414yes—
231C22⋊Dic73C24112yes—
232C22⋊Dic73C24124yes—
233#11924005C24112yes—
234#11924005C24112yes—
235#11924005C24124yes—
236#11924005C24124yes—
237C4×Dic73C2414yes—
238C4×Dic73C24112yes—
239C4×Dic73C24112yes—
240C4×Dic73C2414yes—
241C4×Dic73C24112yes—
242C4×Dic73C24112yes—
243C4×Dic73C24112yes—
244C4×Dic73C24112yes—
245C4×Dic73C24112yes—
246C24×C73C2413yes—
247C24×C73C2411yescharacteristic
248#41×C73—232no—
249C2×Q8×C73—232no—
250C2×Q8×C73—212no—
251C2×Q8×C73#4118yescomplemented
252C2×Q8×C73C24112yes—
253C2×Q8×C73C2414yes—
254C2×D4×C73—212no—
255C2×D4×C73—212no—
256C2×D4×C73C24112yes—
257C2×D4×C73C24112yes—
258C22×C4×C73—212no—
259C22×C4×C73—212no—
260C22×C4×C73C2411yescharacteristic
261C22×C4×C73C2413yes—
262C22×C4×C73C2413yes—
263C22×C4×C73C2411yescharacteristic
264C22×C4×C73C24112yes—
265C22×C4×C73C24112yes—
266C22×C4×C73C2413yes—
267C4⋊C4×C73C24112yes—
268C4⋊C4×C73C24112yes—
269C22⋊C4×C73C2414yes—
270C22⋊C4×C73C24112yes—
271C22⋊C4×C73C24124yes—
272C42×C73C24112yes—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—26no—
276C23×C73—26no—
277C23×C73—26no—
278C23×C73C2×#4114yes—
279C23×C73C2516yes—
280C23×C73C2512yes—
281C23×C73C2511yescharacteristic
282C22×D73—26no—
283C22×D73—26no—
284C22×D73—26no—
285C22×D73C2516yes—
286Q8×C73—224no—
287Q8×C73C2×#41116yescomplemented
288D4×C73—224no—
289D4×C73—224no—
290C2×C4×C73—22no—
291C2×C4×C73—26no—
292C2×C4×C73—26no—
293C2×C4×C73—22no—
294C2×C4×C73—224no—
295C2×C4×C73—224no—
296C2×C4×C73C2×#41112yes—
297C2×C4×C73C2512yes—
298C2×C4×C73C2516yes—
299C2×C4×C73C2516yes—
300C2×C4×C73C2512yes—
301C2×C4×C73C2516yes—
302C22⋊D73—224no—
303C22⋊D73—224no—
304C22⋊D73—424no—
305C2×Dic73—22no—
306C2×Dic73—26no—
307C2×Dic73—26no—
308C2×Dic73—22no—
309C2×Dic73—26no—
310C2×Dic73—224no—
311C2×Dic73—412no—
312C2×Dic73—412no—
313C2×Dic73C2×#4114yes—
314C2×Dic73C2×#4114yes—
315C2×Dic73C2×#41116yescomplemented
316C2×Dic73C2512yes—
317C2×Dic73C2516yes—
318C2×Dic73C2512yes—
319C2×Dic73C2516yes—
320C2×Dic73C2516yes—
321C2×Dic73C2512yes—
322C2×Dic73C2512yes—
323D292—224no—
324C4×D73—224no—
325C4×D73—224no—
326C4×D73—412no—
327Dic146—224no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—28no—
331C22×C73—26no—
332C22×C73—26no—
333C22×C73—26no—
334C22×C73—412no—
335C22×C73C22×#4114yes—
336C22×C73C22×#4112yes—
337C22×C73C22×#4112yes—
338C22×C73#58512yes—
339C22×C73C2611yescharacteristic
340C2×D73—26no—
341C2×D73—26no—
342C2×D73—26no—
343C2×D73—412no—
344C4×C73—26no—
345C4×C73—22no—
346C4×C73—26no—
347C4×C73—22no—
348C4×C73C22×#41112yes—
349Dic73—26no—
350Dic73—22no—
351Dic73—26no—
352Dic73—22no—
353Dic73—26no—
354Dic73C22×#4114yes—
355Dic73C22×#4114yes—
356C2×#3480—731nomaximal, Sylow
357C2×C73—24no—
358C2×C73—46no—
359C2×C73#348014yescomplemented
360C2×C73C23×#4111yescharacteristic
361C2×C73C23×#4111yescharacteristic
362C2×C73C2×#58511yescharacteristic
363D73—46no—
364#3480—7332no—
365C2×#559—733no—
366C2×#557—731no—
367C2×#556—733no—
368C2×#553—733no—
369C2×#553—733no—
370C2×#550—731no—
371C2×#548—731no—
372C2×#548D7311yescharacteristic, complemented
373C2×#532—733no—
374C2×#529—733no—
375C2×#529—733no—
376C2×C4×#41—731no—
377C2×C4×#41—731no—
378C2×C4×#41—733no—
379C22×C4×Q8—731no—
380C73C2×#348011yescharacteristic, complemented, Sylow
381C22×#41—731no—
382C22×#41—733no—
383C22×#41C2×D7311yescharacteristic
384C23×Q8C2×D7311yescharacteristic
385#559—7348no—
386#557—7316no—
387#556—7348no—
388#553—7348no—
389#553—7348no—
390#550—7316no—
391#548—7316no—
392#548C2×D73116yescomplemented
393#532—7348no—
394C2×C4⋊Q8—733no—
395C2×#127—733no—
396#529—7348no—
397#529—7348no—
398C2×#126—736no—
399C2×#126—736no—
400C2×#125—733no—
401C2×#125—733no—
402C2×#124—733no—
403C2×#124—736no—
404C2×#124C2×D7313yes—
405C2×#123—736no—
406C2×#123—736no—
407C2×C22⋊Q8—733no—
408C2×C22⋊Q8C2×D7313yes—
409C2×#121—733no—
410C2×#121—736no—
411C2×#121—733no—
412C2×#121—733no—
413C2×#121C2×D7313yes—
414C4×#41—7316no—
415C4×#41—7316no—
416C4×#41—7348no—
417C2×C4×Q8—731no—
418C2×C4×Q8—733no—
419C2×C4×Q8—731no—
420C2×C4×Q8—733no—
421C2×C4×Q8—7316no—
422C2×C4×Q8—731no—
423C2×C4×Q8—733no—
424C2×C4×Q8—733no—
425C2×C4×Q8C2×D7311yescharacteristic
426C2×C4×D4—733no—
427C2×C4×D4—733no—
428C2×C4×D4—733no—
429C2×C4×D4—733no—
430C2×C4×D4—733no—
431C2×C4×D4—733no—
432C2×C4×D4—733no—
433C2×C4×D4—733no—
434C2×C4×D4—736no—
435C2×C4×D4—733no—
436C2×C4×D4C2×D7313yes—
437C2×#117—733no—
438C2×#117—733no—
439C2×#117—733no—
440C2×#117—731no—
441C2×#117—733no—
442C22×C4⋊C4—733no—
443C22×C42—733no—
444C22×C42—733no—
445C22×C42—733no—
446C2×#41—28no—
447C2×#41—738no—
448C2×#41—7324no—
449C2×#41—14624no—
450C2×#41—1468no—
451C2×#41C22×D7318yes—
452C22×Q8—28no—
453C22×Q8—733no—
454C22×Q8C22×D7313yes—
455C22×Q8C22×D7318yes—
456C22×Q8C22×D7311yescharacteristic
457C22×D4—736no—
458C22×D4—733no—
459C22×D4—733no—
460C22×D4—733no—
461C22×D4C22×D7313yes—
462C22×D4C22×D7313yes—
463C23×C4—733no—
464C23×C4—733no—
465C23×C4—733no—
466C23×C4—731no—
467C23×C4—733no—
468C23×C4—733no—
469C23×C4—733no—
470C23×C4C22×D7313yes—
471C23×C4C22×D7313yes—
472C4⋊Q8—7324no—
473#127—7324no—
474#126—7348no—
475#126—7348no—
476#125—7324no—
477#125—7324no—
478#124—7324no—
479#124—7348no—
480#124C22×D73124yes—
481#123—7348no—
482#123—7348no—
483C22⋊Q8—7324no—
484C22⋊Q8C22×D73124yes—
485#121—7324no—
486#121—7348no—
487#121—7324no—
488#121—7324no—
489#121C22×D73124yes—
490C4×Q8—738no—
491C4×Q8—7324no—
492C4×Q8—738no—
493C4×Q8—7324no—
494C4×Q8—738no—
495C4×Q8—7324no—
496C4×Q8—7324no—
497C4×Q8C22×D7318yes—
498C4×D4—7324no—
499C4×D4—7324no—
500C4×D4—7324no—
501C4×D4—7324no—
502C4×D4—7324no—
503C4×D4—7324no—
504C4×D4—7324no—
505C4×D4—7324no—
506C4×D4—7348no—
507C4×D4—7324no—
508C4×D4C22×D73124yes—
509#117—7324no—
510#117—7324no—
511#117—7324no—
512#117—738no—
513#117—7324no—
514C2×C4⋊C4—733no—
515C2×C4⋊C4—733no—
516C2×C4⋊C4—736no—
517C2×C4⋊C4—7324no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—733no—
521C2×C4⋊C4—733no—
522C2×C4⋊C4—733no—
523C2×C4⋊C4—733no—
524C2×C4⋊C4—736no—
525C2×C4⋊C4C22×D7313yes—
526C2×C4⋊C4C22×D7313yes—
527C2×C22⋊C4—731no—
528C2×C22⋊C4—733no—
529C2×C22⋊C4—736no—
530C2×C22⋊C4—733no—
531C2×C22⋊C4—736no—
532C2×C22⋊C4—733no—
533C2×C22⋊C4—736no—
534C2×C22⋊C4C22×D7311yescharacteristic
535C2×C22⋊C4C22×D7313yes—
536C2×C22⋊C4C22×D7316yes—
537C2×C42—731no—
538C2×C42—731no—
539C2×C42—733no—
540C2×C42—733no—
541C2×C42—733no—
542C2×C42—733no—
543C2×C42—733no—
544C2×C42—733no—
545C2×C42—733no—
546C2×C42—7324no—
547C2×C42—7324no—
548C2×C42—7324no—
549C2×C42C22×D7313yes—
550C24—733no—
551C24C23×D7313yes—
552C24C23×D7311yescharacteristic
553#41—232no—
554#41—14696no—
555#41—14632no—
556C2×Q8—232no—
557C2×Q8—212no—
558C2×Q8—7312no—
559C2×Q8—14612no—
560C2×Q8#1192402718yescomplemented
561C2×Q8C23×D73112yes—
562C2×Q8C23×D7314yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—29212no—
566C2×D4—7324no—
567C2×D4—7312no—
568C2×D4—7312no—
569C2×D4—7312no—
570C2×D4—14612no—
571C2×D4—14612no—
572C2×D4—14612no—
573C2×D4C23×D73112yes—
574C2×D4C23×D73112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—2926no—
578C22×C4—2926no—
579C22×C4—2926no—
580C22×C4—7312no—
581C22×C4—7312no—
582C22×C4—7312no—
583C22×C4—738no—
584C22×C4—734no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—7312no—
588C22×C4—731no—
589C22×C4—731no—
590C22×C4—733no—
591C22×C4—733no—
592C22×C4—733no—
593C22×C4—7312no—
594C22×C4—7312no—
595C22×C4—14612no—
596C22×C4—14612no—
597C22×C4—14612no—
598C22×C4C23×D73112yes—
599C22×C4C23×D73112yes—
600C22×C4C23×D7311yescharacteristic
601C22×C4C23×D7313yes—
602C22×C4C23×D7311yescharacteristic
603C22×C4C23×D7313yes—
604C22×C4C23×D7313yes—
605C4⋊C4—734no—
606C4⋊C4—734no—
607C4⋊C4—7312no—
608C4⋊C4—7312no—
609C4⋊C4—7324no—
610C4⋊C4—7312no—
611C4⋊C4—7312no—
612C4⋊C4—7324no—
613C4⋊C4—7312no—
614C4⋊C4—7312no—
615C4⋊C4C23×D73112yes—
616C4⋊C4C23×D73112yes—
617C22⋊C4—734no—
618C22⋊C4—7312no—
619C22⋊C4—7324no—
620C22⋊C4—7312no—
621C22⋊C4—7324no—
622C22⋊C4—7312no—
623C22⋊C4—7324no—
624C22⋊C4C23×D7314yes—
625C22⋊C4C23×D73112yes—
626C22⋊C4C23×D73124yes—
627C42—734no—
628C42—734no—
629C42—7312no—
630C42—7312no—
631C42—7312no—
632C42—7312no—
633C42—7312no—
634C42—7312no—
635C42—7312no—
636C42C23×D73112yes—
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—736no—
643C23—1466no—
644C23—1466no—
645C23—1466no—
646C23#41×D7314yes—
647C23C24×D7316yes—
648C23C24×D7312yes—
649C23C24×D7311yescharacteristic
650Q8—224no—
651Q8—14624no—
652Q8C2×#11924027116yescomplemented
653D4—224no—
654D4—224no—
655D4—29224no—
656D4—14624no—
657D4—14624no—
658D4—14624no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—29212no—
666C2×C4—29212no—
667C2×C4—29212no—
668C2×C4—734no—
669C2×C4—734no—
670C2×C4—7316no—
671C2×C4—732no—
672C2×C4—732no—
673C2×C4—732no—
674C2×C4—732no—
675C2×C4—736no—
676C2×C4—736no—
677C2×C4—736no—
678C2×C4—14624no—
679C2×C4—14624no—
680C2×C4—1466no—
681C2×C4—1462no—
682C2×C4—1466no—
683C2×C4—1462no—
684C2×C4—1466no—
685C2×C4—14624no—
686C2×C4C2×#11924027112yes—
687C2×C4C24×D7312yes—
688C2×C4C24×D7316yes—
689C2×C4C24×D7312yes—
690C2×C4C24×D7316yes—
691C2×C4C24×D7316yes—
692C22—28no—
693C22—22no—
694C22—22no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—29212no—
700C22—1466no—
701C22—1466no—
702C22—1466no—
703C22C2×#41×D7314yes—
704C22C2×#41×D7312yes—
705C22C22×#1192402712yes—
706C22#1798942412yes—
707C22C25×D7311yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—734no—
713C4—734no—
714C4—1466no—
715C4—1462no—
716C4—1466no—
717C4—1462no—
718C4—1466no—
719C4C22×#11924027112yes—
720C2—24no—
721C2—46no—
722C2—2926no—
723C2#2262352114yesdirect product factor
724C2C22×#41×D7311yescharacteristic
725C2C23×#1192402711yescharacteristic
726C2C2×#1798942411yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#548×C73C2
socleC23×C73C25
hypercenterC2×#548D73
hypocenterC73C2×#3480
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22623521C2direct (N × H)
2. C2×#17989319C2semidirect
3. C2×#17989313C2semidirect
4. C2×#17989308C2semidirect
5. C2×#17989289C2semidirect
6. C2×#17989283C2semidirect
7. C2×#17989256C2semidirect
8. C2×#17989248C2semidirect
9. C2×#17989132C2semidirect
10. C2×#17989123C2semidirect
11. C2×#17989116C2semidirect
12. C2×#41×Dic73C2semidirect
13. C2×C4×#11924029C2semidirect
14. C2×C4×#11924027C2semidirect
15. C22×Q8×Dic73C2semidirect
16. C2×#548×C73C2semidirect
19. #17989319C22semidirect
20. #17989313C22semidirect
21. #17989308C22semidirect
22. #17989289C22semidirect
23. #17989283C22semidirect
24. #17989256C22semidirect
25. #17989248C22semidirect
26. #17989132C22semidirect
29. #17989123C22semidirect
30. #17989116C22semidirect
44. #41×Dic73C22semidirect
45. C4×#11924029C22semidirect
46. C4×#11924027C22semidirect
52. C2×Q8×Dic73C22semidirect
76. #548×C73C22semidirect
202. C22×Dic73#41semidirect
251. C2×Q8×C73#41semidirect
287. Q8×C73C2×#41semidirect
315. C2×Dic73C2×#41semidirect
359. C2×C73#3480semidirect
372. C2×#548D73semidirect
380. C73C2×#3480semidirect
392. #548C2×D73semidirect
560. C2×Q8#11924027semidirect
652. Q8C2×#11924027semidirect
723. C2#22623521direct (N × H)

Maximal subgroups

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

subgroupindex
#226235212
C2×#179893192
C2×#179893132
C2×#179893082
C2×#179892892
C2×#179892832
C2×#179892562
C2×#179892482
C2×#179891322
C2×#179891232
C2×#179891162
C2×#41×Dic732
C2×C4×#119240292
C2×C4×#119240272
C22×Q8×Dic732
C2×#548×C732
C2×#348073