Finite Group Databasebeta

← C2×#11737662 #14222060

Subgroups — C2×#11737662 #14222060

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90518C211yesmaximal, characteristic
2C2×#90316C211yesmaximal, characteristic, complemented
3C2×C7×#452C211yesmaximal, characteristic
4C2×#90011C211yesmaximal, characteristic
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×Q16×Dic7C211yesmaximal, characteristic, complemented
7C2×#89934C211yesmaximal, characteristic, complemented
8C2×#89936C211yesmaximal, characteristic, complemented
9C2×#89815C211yesmaximal, characteristic, complemented
10#11737662C2116yesmaximal, direct product factor
11C2×#89568C211yesmaximal, characteristic, complemented
12C2×#89561C211yesmaximal, characteristic, complemented
13C2×#89538C211yesmaximal, characteristic, complemented
14C2×#89530C211yesmaximal, characteristic, complemented
15C2×#89494C211yesmaximal, characteristic, complemented
16C2×#89492C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21#90518—24no—
22#90518C2218yes—
23C2×Q8×Dic7C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×#6507C2211yescharacteristic
27C22×#1144C2211yescharacteristic
28C2×D4×Dic7—21no—
29C2×D4×Dic7—21no—
30C2×D4×Dic7C2211yescharacteristic
31C2×D4×Dic7C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C2×#6489—21no—
34C2×#6489C2211yescharacteristic
35C22×C4⋊Dic7—21no—
36C22×C4⋊Dic7C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38#90316—24no—
39#90316C2218yescomplemented
40C2×#6453—21no—
41C2×#6453C2211yescharacteristic
42C2×#6452—21no—
43C2×#6450C2211yescharacteristic
44C2×#6442—21no—
45C2×#6442—21no—
46C7×#452C2218yes—
47C2×C7×#103C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50#90011C2218yes—
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56Q16×Dic7C2218yescomplemented
57#89954C2218yescomplemented
58#89936C2218yescomplemented
59#89934C2218yescomplemented
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6389C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89815C2218yescomplemented
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71#89568C2218yescomplemented
72#89561C2218yescomplemented
73#89538C2218yescomplemented
74#89530C2218yescomplemented
75#89494C2218yescomplemented
76#89492C2218yescomplemented
77C2×#3120—71nomaximal, Sylow
78C2×C7×#41—24no—
79C2×C7×#41—24no—
80C2×C7×#41—22no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2311yescharacteristic
84C22×C7×D4—21no—
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C23×Dic7—21no—
89C23×Dic7—21no—
90C23×Dic7—21no—
91C22×Dic14C2311yescharacteristic
92C2×C7×Q16—24no—
93C2×C7×Q16C2314yes—
94C2×C7×SD16—24no—
95C2×C7×SD16C2314yes—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×C22⋊Q8—22no—
99C7×C22⋊Q8C2314yes—
100C2×C7×C4⋊C4—21no—
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7D411yescharacteristic
107C2×C22⋊Dic7D411yescharacteristic
108Q8×Dic7—22no—
109Q8×Dic7—22no—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112Q8×Dic7C2314yes—
113Q8×Dic7C2314yes—
114#6507—22no—
115#6507C2314yes—
116C2×#1144—24no—
117C2×#1144C2314yes—
118D4×Dic7—28no—
119D4×Dic7—28no—
120D4×Dic7—22no—
121D4×Dic7—22no—
122D4×Dic7C2314yes—
123D4×Dic7C2314yes—
124C2×#1142—24no—
125C2×#1142C2314yes—
126#6489—28no—
127#6489D414yes—
128#6489C2314yes—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—22no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7—28no—
136C2×C4⋊Dic7D411yescharacteristic
137C2×C4⋊Dic7D411yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2314yes—
142#6487—22no—
143#6487C2314yes—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×C4×Dic7—21no—
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157#6453—28no—
158#6453—22no—
159#6453C2314yes—
160#6452—28no—
161#6450—22no—
162#6450C2314yes—
163#6442—28no—
164#6442—28no—
165C7×#103C2314yes—
166C7×#102C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6406C2314yes—
172C22⋊(C7⋊C8)C2314yes—
173#6392C2314yes—
174#6392C2314yes—
175#6390C2314yes—
176#6390C2314yes—
177#6389C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180C8×Dic7C2314yes—
181#6382C2314yes—
182#6382C2314yes—
183C2×#541—71no—
184C2×#520—71no—
185#3120—716no—
186C2×#484—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#462—71no—
191C2×#461—71no—
192C2×#452—71no—
193C2×#452D711yescharacteristic
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C7×#41—216no—
202C7×#41—28no—
203C7×#41—28no—
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8#4114yes—
210C2×C7×Q8C2412yes—
211C2×C7×Q8C2412yes—
212C2×C7×D4—28no—
213C2×C7×D4—24no—
214C2×C7×D4—21no—
215C2×C7×D4—22no—
216C2×C7×D4#4114yes—
217C2×C7×D4C2412yes—
218C22×C4×C7—28no—
219C22×C4×C7—21no—
220C22×C4×C7—24no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2411yescharacteristic
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—24no—
234C22×Dic7—24no—
235C22×Dic7—24no—
236C22×Dic7—82no—
237C22×Dic7—82no—
238C22×Dic7—82no—
239C22×Dic7C2×D411yescharacteristic
240C22×Dic7C2×D411yescharacteristic
241C22×Dic7C2×D411yescharacteristic
242C22×Dic7C2×D411yescharacteristic
243C2×Dic14—22no—
244C2×Dic14—22no—
245C2×Dic14—21no—
246C2×Dic14C2412yes—
247C7×Q16—28no—
248C7×SD16—28no—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C22⋊Dic7—24no—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7C2×D414yes—
261C22⋊Dic7C2×D414yes—
262#1144—28no—
263#1142—28no—
264C4⋊Dic7—21no—
265C4⋊Dic7—24no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2×D414yes—
273C4⋊Dic7C2×D414yes—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7C2×D412yes—
287C4×Dic7C2×D412yes—
288C4×Dic7C2412yes—
289C4×Dic7C2412yes—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294C22×#41C2×D711yescharacteristic
295C22×Q16—71no—
296C22×Q16C2×D711yescharacteristic
297C22×SD16—71no—
298C22×SD16C2×D711yescharacteristic
299#541—78no—
300#541—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#126—141no—
304C2×#125—71no—
305C2×#125—141no—
306C2×#125—141no—
307C2×C22⋊Q8—71no—
308C2×C22⋊Q8C2×D711yescharacteristic
309#520—78no—
310#520—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—71no—
315C2×C4×D4—71no—
316C2×C4×D4—71no—
317C2×C4×D4—141no—
318C2×C4×D4—141no—
319C2×#117—71no—
320C2×#117—141no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—141no—
323#484—78no—
324#483—78no—
325#479—78no—
326#478—78no—
327#462—78no—
328#461—78no—
329#452—78no—
330#452C2×D718yes—
331#441—78no—
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103C2×D711yescharacteristic
348C2×#102—71no—
349C2×#102C2×D711yescharacteristic
350C2×C22⋊C8—71no—
351C2×C22⋊C8C2×D711yescharacteristic
352C2×#97—71no—
353C2×C4×C8—71no—
354C23×C7—22no—
355C23×C7—24no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C7×Q8—24no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—22no—
367C7×Q8—42no—
368C7×Q8C2×#4114yes—
369C7×D4—216no—
370C7×D4—24no—
371C7×D4—22no—
372C7×D4C2×#4114yes—
373C2×C4×C7—216no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—22no—
377C2×C4×C7—24no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4112yes—
387C2×C4×C7C2×#4112yes—
388C2×C4×C7C2511yescharacteristic
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—42no—
398C2×Dic7—42no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—84no—
402C2×Dic7—84no—
403C2×Dic7—84no—
404C2×Dic7C22×D412yes—
405C2×Dic7C22×D412yes—
406C2×Dic7C22×D412yes—
407C2×Dic7C22×D412yes—
408Dic14—22no—
409Dic14—22no—
410Dic14—42no—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C2×#41—24no—
416C2×#41—24no—
417C2×#41—22no—
418C2×#41C22×D714yes—
419C22×Q8—71no—
420C22×Q8C22×D711yescharacteristic
421C22×Q8C22×D711yescharacteristic
422C22×D4—21no—
423C22×D4C22×D711yescharacteristic
424C23×C4—21no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4—141no—
428C23×C4C22×D711yescharacteristic
429C2×Q16—24no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16C22×D714yes—
433C2×SD16—24no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16C22×D714yes—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8C22×D711yescharacteristic
440C22×C8C22×D711yescharacteristic
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#125—74no—
446#125—142no—
447#125—148no—
448#125—148no—
449C22⋊Q8—22no—
450C22⋊Q8—74no—
451C22⋊Q8—142no—
452C22⋊Q8C22×D714yes—
453C4×Q8—74no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—142no—
458C4×Q8—142no—
459C4×Q8—142no—
460C4×Q8—142no—
461C4×D4—74no—
462C4×D4—74no—
463C4×D4—142no—
464C4×D4—142no—
465C4×D4—148no—
466C4×D4—148no—
467#117—74no—
468#117—74no—
469#117—148no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—74no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—148no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4—141no—
489C2×C4⋊C4C22×D711yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—71no—
492C2×C22⋊C4—71no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C42—71no—
497C2×C42—71no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42—141no—
502#107—74no—
503#107—74no—
504#106—74no—
505#106—74no—
506C4⋊C8—74no—
507C4⋊C8—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#103C22×D714yes—
514#102—74no—
515#102C22×D714yes—
516C22⋊C8—74no—
517C22⋊C8C22×D714yes—
518#97—74no—
519C4×C8—74no—
520C22×C7—22no—
521C22×C7—24no—
522C22×C7—22no—
523C22×C7—22no—
524C22×C7—44no—
525C22×C7—48no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7#52512yes—
529C22×C7#57712yes—
530C22×C7#57812yes—
531C22×C7C23×D411yescharacteristic
532C4×C7—22no—
533C4×C7—24no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#52512yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C22×#4111yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7—22no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547C24—21no—
548C24D4×D711yescharacteristic
549#41—216no—
550#41—28no—
551#41—28no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—72no—
558C2×Q8—141no—
559C2×Q8—142no—
560C2×Q8—142no—
561C2×Q8#115914yes—
562C2×Q8C23×D712yes—
563C2×Q8C23×D712yes—
564C2×D4—28no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4#115914yes—
569C2×D4C23×D712yes—
570C22×C4—28no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—71no—
581C22×C4—144no—
582C22×C4—144no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—144no—
588C22×C4—562no—
589C22×C4—562no—
590C22×C4—562no—
591C22×C4D4×D712yes—
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D712yes—
594C22×C4C23×D711yescharacteristic
595Q16—28no—
596Q16—148no—
597SD16—28no—
598SD16—148no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—72no—
602C2×C8—72no—
603C2×C8—142no—
604C2×C8—142no—
605C2×C8C23×D712yes—
606C2×C8C23×D712yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—74no—
610C4⋊C4—74no—
611C4⋊C4—72no—
612C4⋊C4—72no—
613C4⋊C4—72no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—141no—
625C4⋊C4—141no—
626C4⋊C4—141no—
627C4⋊C4C23×D712yes—
628C22⋊C4—24no—
629C22⋊C4—74no—
630C22⋊C4—74no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C42—72no—
635C42—72no—
636C42—72no—
637C42—72no—
638C42—144no—
639C42—144no—
640C42—144no—
641C42—144no—
642C2×C7—42no—
643C2×C7—44no—
644C2×C7#312014yescomplemented
645C2×C7C2×#52511yescharacteristic
646C2×C7C2×#57711yescharacteristic
647C2×C7C2×#57811yescharacteristic
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23C2×D4×D712yes—
656C23C2×D4×D711yescharacteristic
657Q8—24no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—142no—
663Q8—142no—
664Q8—282no—
665Q8C2×#115914yes—
666D4—216no—
667D4—24no—
668D4—22no—
669D4C2×#115914yes—
670C2×C4—216no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—72no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4—564no—
698C2×C4—564no—
699C2×C4—564no—
700C2×C4C2×D4×D712yes—
701C2×C4C2×D4×D711yescharacteristic
702C2×C4C2×#115912yes—
703C2×C4C2×#115912yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—142no—
708C8—142no—
709C7C2×#312011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—24no—
712C22—22no—
713C22—22no—
714C22—42no—
715C22—44no—
716C22—48no—
717C22—42no—
718C22#9027712yes—
719C22#9046212yes—
720C22#9046912yes—
721C22C22×D4×D711yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—142no—
727C4—142no—
728C4—142no—
729C4—142no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4#9027712yes—
735C4C22×#115911yescharacteristic
736C4C22×#115911yescharacteristic
737C2—42no—
738C2—44no—
739C2#1173766214yesdirect product factor
740C2C2×#9027711yescharacteristic
741C2C2×#9046211yescharacteristic
742C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#452C2
socleC23×C7C22×D4
prime radicalC22×C7×#41C22
hypercenterC2×#452D7
hypocenterC7C2×#3120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#90316C2semidirect
5. C2×#89954C2semidirect
6. C2×Q16×Dic7C2semidirect
7. C2×#89934C2semidirect
8. C2×#89936C2semidirect
9. C2×#89815C2semidirect
10. #11737662C2direct (N × H)
11. C2×#89568C2semidirect
12. C2×#89561C2semidirect
13. C2×#89538C2semidirect
14. C2×#89530C2semidirect
15. C2×#89494C2semidirect
16. C2×#89492C2semidirect
39. #90316C22semidirect
56. Q16×Dic7C22semidirect
57. #89954C22semidirect
58. #89936C22semidirect
59. #89934C22semidirect
68. #89815C22semidirect
71. #89568C22semidirect
72. #89561C22semidirect
73. #89538C22semidirect
74. #89530C22semidirect
75. #89494C22semidirect
76. #89492C22semidirect
644. C2×C7#3120semidirect
709. C7C2×#3120semidirect
739. C2#11737662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905182
C2×#903162
C2×C7×#4522
C2×#900112
C2×#899542
C2×Q16×Dic72
C2×#899342
C2×#899362
C2×#898152
#117376622
C2×#895682
C2×#895612
C2×#895382
C2×#895302
C2×#894942
C2×#894922
C2×#31207