Finite Group Databasebeta

← C2×#11736830 #14222061

Subgroups — C2×#11736830 #14222061

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×#90214C211yesmaximal, characteristic
2C2×#90209C211yesmaximal, characteristic, complemented
3C2×C7×#433C211yesmaximal, characteristic, complemented
4#11736830C2116yesmaximal, direct product factor
5C2×#89601C211yesmaximal, characteristic, complemented
6C2×#89621C211yesmaximal, characteristic, complemented
7C2×#89619C211yesmaximal, characteristic, complemented
8C2×#89613C211yesmaximal, characteristic, complemented
9C2×#89505C211yesmaximal, characteristic
10C2×#89505C211yesmaximal, characteristic
11C2×#89494C211yesmaximal, characteristic, complemented
12C2×#89493C211yesmaximal, characteristic, complemented
13C2×#89488C211yesmaximal, characteristic, complemented
14C2×#89482C211yesmaximal, characteristic, complemented
15C2×C4×Dic28C211yesmaximal, characteristic, complemented
16C2×C4×#1132C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C2×C7×#117C2211yescharacteristic
19C22×C4⋊Dic7C2211yescharacteristic
20C2×#6487C2211yescharacteristic
21C2×#6487C2211yescharacteristic
22C22×Dic28C2211yescharacteristic
23C22×Dic28C2211yescharacteristic
24C22×#1132C2211yescharacteristic
25C22×#1132C2211yescharacteristic
26#90214—24no—
27#90214C2218yes—
28#90209—24no—
29#90209C2218yescomplemented
30C2×#6455—21no—
31C2×D7×C4⋊C4—21no—
32C2×#6452—21no—
33C2×#6452—21no—
34C2×(C22⋊D7)⋊C4—21no—
35C2×(C22⋊D7)⋊C4—21no—
36C2×#6442—21no—
37C2×#6442—21no—
38C2×C4×D28C2211yescharacteristic
39C2×C4×D28C2211yescharacteristic
40C2×#6433C2211yescharacteristic
41C2×#6432C2211yescharacteristic
42C2×C4×Dic14C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C7×#433C2218yescomplemented
47C2×C7×C4⋊C8C2211yescharacteristic
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×C7×#97C2211yescharacteristic
52C2×C4×C7×C8C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6392C2211yescharacteristic
57C2×#6391C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6390C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65#89621C2218yescomplemented
66#89619C2218yescomplemented
67#89613C2218yescomplemented
68#89601C2218yescomplemented
69#89505C2218yes—
70#89505C2218yes—
71#89494C2218yescomplemented
72#89493C2218yescomplemented
73#89488C2218yescomplemented
74#89482C2218yescomplemented
75C4×Dic28C2218yescomplemented
76C4×#1132C2218yescomplemented
77C2×#3120—71nomaximal, Sylow
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7—21no—
80C23×Dic7—21no—
81C2×#1157—22no—
82C2×#1157—24no—
83C2×#1157—24no—
84C2×#1157C2314yes—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×Dic14C2311yescharacteristic
90C22×Dic14C2311yescharacteristic
91C22×Dic14C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C7×#117D414yes—
97C7×#117C2314yes—
98C2×C7×C4⋊C4D411yescharacteristic
99C2×C7×C4⋊C4D411yescharacteristic
100C2×C7×C22⋊C4D411yescharacteristic
101C2×C7×C22⋊C4D411yescharacteristic
102C2×C42×C7C2311yescharacteristic
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106C2×(C2×D7)⋊C4—21no—
107C2×(C2×D7)⋊C4—21no—
108C2×C4⋊Dic7—21no—
109C2×C4⋊Dic7—21no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7C2311yescharacteristic
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2314yes—
117#6487—22no—
118#6487—22no—
119#6487C2314yes—
120#6487C2314yes—
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C2×C4×Dic7—21no—
132C2×C4×Dic7—21no—
133C2×Dic28—24no—
134C2×Dic28—24no—
135C2×Dic28C2314yes—
136C2×Dic28C2314yes—
137C2×#1132—24no—
138C2×#1132—24no—
139C2×#1132C2314yes—
140C2×#1132C2314yes—
141#6455—28no—
142D7×C4⋊C4—28no—
143#6452—28no—
144#6452—28no—
145(C22⋊D7)⋊C4—28no—
146(C22⋊D7)⋊C4—28no—
147#6442—28no—
148#6442—28no—
149C4×D28—22no—
150C4×D28—22no—
151C4×D28C2314yes—
152C4×D28C2314yes—
153#6433—22no—
154#6433C2314yes—
155#6432—22no—
156#6432C2314yes—
157C4×Dic14—22no—
158C4×Dic14—22no—
159C4×Dic14—22no—
160C4×Dic14—22no—
161C4×Dic14C2314yes—
162C4×Dic14C2314yes—
163C4×Dic14C2314yes—
164C4×Dic14C2314yes—
165C7×C4⋊C8C2314yes—
166C7×C4⋊C8C2314yes—
167C7×C22⋊C8C2314yes—
168C7×C22⋊C8C2314yes—
169C7×#97C2314yes—
170C4×C7×C8C2314yes—
171#6395C2314yes—
172#6395C2314yes—
173#6392C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6391C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6390C2314yes—
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×#452—71no—
194C2×#441—71no—
195C2×#440—71no—
196C2×C4×Q16—71no—
197C2×C4×SD16—71no—
198C2×#433D711yescharacteristic, complemented
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2412yes—
210C22×C4×C7C2411yescharacteristic
211C2×C22⋊D7—28no—
212C2×C22⋊D7—24no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—24no—
221C22×Dic7—82no—
222#1157—216no—
223#1157—28no—
224#1157—28no—
225C2×D28—21no—
226C2×D28—22no—
227C2×D28#4114yes—
228C2×D28C2412yes—
229C2×C4×D7—28no—
230C2×C4×D7—24no—
231C2×C4×D7—24no—
232C2×C4×D7—24no—
233C2×C4×D7—82no—
234C2×C4×D7—82no—
235C2×Dic14—21no—
236C2×Dic14—22no—
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—21no—
242C2×Dic14—21no—
243C2×Dic14#4114yes—
244C2×Dic14C2412yes—
245C2×Dic14C2412yes—
246C2×Dic14C2412yes—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C7×C4⋊C4C2×D414yes—
256C7×C4⋊C4C2×D414yes—
257C7×C22⋊C4C2×D414yes—
258C7×C22⋊C4C2×D414yes—
259C42×C7C2×D412yes—
260C42×C7C2×D412yes—
261C42×C7C2412yes—
262C42×C7C2412yes—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—24no—
272C4⋊Dic7—24no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277C4⋊Dic7C2412yes—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286C4×Dic7—24no—
287C4×Dic7—24no—
288C4×Dic7—24no—
289C4×Dic7—24no—
290Dic28—28no—
291Dic28—28no—
292#1132—28no—
293#1132—28no—
294C22×#41—71no—
295C22×Q16—71no—
296C22×Q16—71no—
297C22×SD16—71no—
298C22×SD16—71no—
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⋊Q8—71no—
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—141no—
320C2×#117C2×D711yescharacteristic
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#452—78no—
331#441—78no—
332#440—78no—
333C4×Q16—78no—
334C4×SD16—78no—
335#433C2×D718yescomplemented
336C2×#107—71no—
337C2×#107—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×C4⋊C8C2×D711yescharacteristic
341C2×C4⋊C8C2×D711yescharacteristic
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8C2×D711yescharacteristic
351C2×C22⋊C8C2×D711yescharacteristic
352C2×#97C2×D711yescharacteristic
353C2×C4×C8C2×D711yescharacteristic
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C22×D7—24no—
360C22×D7—22no—
361C22×D7—42no—
362C22×D7—42no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—24no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C2×#4112yes—
378C2×C4×C7C2×#4112yes—
379C2×C4×C7C2511yescharacteristic
380C22⋊D7—216no—
381C2×Dic7—24no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—84no—
396D28—24no—
397D28—22no—
398D28C2×#4114yes—
399C4×D7—216no—
400C4×D7—84no—
401C4×D7—84no—
402Dic14—24no—
403Dic14—22no—
404Dic14—22no—
405Dic14—22no—
406Dic14—22no—
407Dic14—22no—
408Dic14—42no—
409Dic14—42no—
410Dic14C2×#4114yes—
411C7×C8—22no—
412C7×C8—22no—
413C7×C8—22no—
414C7×C8—22no—
415C2×#41—74no—
416C2×#41—144no—
417C2×#41—144no—
418C2×#41—142no—
419C22×Q8—71no—
420C22×Q8—71no—
421C22×Q8—71no—
422C22×D4—71no—
423C22×D4—141no—
424C23×C4—141no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4—141no—
428C23×C4C22×D711yescharacteristic
429C2×Q16—74no—
430C2×Q16—74no—
431C2×Q16—144no—
432C2×Q16—144no—
433C2×SD16—74no—
434C2×SD16—74no—
435C2×SD16—144no—
436C2×SD16—144no—
437C22×C8C22×D711yescharacteristic
438C22×C8C22×D711yescharacteristic
439C22×C8C22×D711yescharacteristic
440C22×C8C22×D711yescharacteristic
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443#126—148no—
444#126—148no—
445#125—74no—
446#125—148no—
447#125—148no—
448#125—142no—
449C22⋊Q8—74no—
450C22⋊Q8—74no—
451C22⋊Q8—142no—
452C22⋊Q8—142no—
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—148no—
464C4×D4—148no—
465C4×D4—142no—
466C4×D4—142no—
467#117—148no—
468#117D2814yes—
469#117C22×D714yes—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—142no—
477C2×C4⋊C4—141no—
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—148no—
488C2×C4⋊C4D2811yescharacteristic
489C2×C4⋊C4D2811yescharacteristic
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C22⋊C4D2811yescharacteristic
495C2×C22⋊C4D2811yescharacteristic
496C2×C42—141no—
497C2×C42—141no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42C22×D711yescharacteristic
501C2×C42C22×D711yescharacteristic
502#107—74no—
503#107—74no—
504#106—74no—
505#106—74no—
506C4⋊C8C22×D714yes—
507C4⋊C8C22×D714yes—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#103—74no—
514#102—74no—
515#102—74no—
516C22⋊C8C22×D714yes—
517C22⋊C8C22×D714yes—
518#97C22×D714yes—
519C4×C8C22×D714yes—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—44no—
524C22×C7#52512yes—
525C22×C7#57712yes—
526C22×C7#57812yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—24no—
529C2×D7—48no—
530C2×D7—42no—
531C2×D7—42no—
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—22no—
537C4×C7#52512yes—
538C4×C7C22×#4111yescharacteristic
539C4×C7C22×#4111yescharacteristic
540Dic7—24no—
541Dic7—42no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546Dic7—42no—
547C24—141no—
548C24C2×D2811yescharacteristic
549#41—148no—
550#41—148no—
551#41—1416no—
552C2×Q8—74no—
553C2×Q8—72no—
554C2×Q8—72no—
555C2×Q8—72no—
556C2×Q8—141no—
557C2×Q8—141no—
558C2×Q8—141no—
559C2×Q8—142no—
560C2×Q8—142no—
561C2×Q8—142no—
562C2×Q8—142no—
563C2×Q8—142no—
564C2×D4—74no—
565C2×D4—72no—
566C2×D4—148no—
567C2×D4—144no—
568C2×D4—141no—
569C2×D4—142no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—148no—
573C22×C4—141no—
574C22×C4—144no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
579C22×C4—141no—
580C22×C4—141no—
581C22×C4—144no—
582C22×C4—144no—
583C22×C4—144no—
584C22×C4—562no—
585C22×C4—562no—
586C22×C4—562no—
587C22×C4C2×D2812yes—
588C22×C4C2×D2811yescharacteristic
589C22×C4C2×D2811yescharacteristic
590C22×C4C2×D2811yescharacteristic
591C22×C4C2×D2811yescharacteristic
592C22×C4C2×D2811yescharacteristic
593C22×C4C23×D712yes—
594C22×C4C23×D711yescharacteristic
595Q16—148no—
596Q16—148no—
597SD16—148no—
598SD16—148no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C2×C8C23×D712yes—
606C2×C8C23×D712yes—
607C4⋊C4—72no—
608C4⋊C4—72no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4—141no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4C2×D2814yes—
627C4⋊C4C2×D2814yes—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4C2×D2814yes—
633C22⋊C4C2×D2814yes—
634C42—144no—
635C42—144no—
636C42—144no—
637C42—144no—
638C42C2×D2812yes—
639C42C2×D2812yes—
640C42C23×D712yes—
641C42C23×D712yes—
642C2×C7—42no—
643C2×C7#312014yescomplemented
644C2×C7C2×#52511yescharacteristic
645C2×C7C2×#57711yescharacteristic
646C2×C7C2×#57811yescharacteristic
647D7—44no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—144no—
652C23—142no—
653C23—282no—
654C23—282no—
655C23C22×D2812yes—
656C23C22×D2811yescharacteristic
657Q8—74no—
658Q8—144no—
659Q8—142no—
660Q8—142no—
661Q8—142no—
662Q8—142no—
663Q8—142no—
664Q8—282no—
665Q8—282no—
666D4—74no—
667D4—1416no—
668D4—144no—
669D4—142no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—1416no—
679C2×C4—144no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—564no—
694C2×C4—564no—
695C2×C4—564no—
696C2×C4C22×D2812yes—
697C2×C4C22×D2812yes—
698C2×C4C22×D2812yes—
699C2×C4C22×D2812yes—
700C2×C4C22×D2812yes—
701C2×C4C22×D2811yescharacteristic
702C2×C4D7×#4112yes—
703C2×C4D7×#4112yes—
704C2×C4C24×D711yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8—22no—
709C7C2×#312011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—144no—
715C22—282no—
716C22—282no—
717C22—288no—
718C22#9021512yes—
719C22#9044212yes—
720C22#9044412yes—
721C22C23×D2811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—144no—
728C4—282no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4—282no—
733C4—282no—
734C4#9021512yes—
735C4C2×D7×#4111yescharacteristic
736C4C2×D7×#4111yescharacteristic
737C2—42no—
738C2—284no—
739C2#1173683014yesdirect product factor
740C2C2×#9021511yescharacteristic
741C2C2×#9044211yescharacteristic
742C2C2×#9044411yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#433C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
hypercenterC2×#433D7
hypocenterC7C2×#3120
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#90209C2semidirect
3. C2×C7×#433C2semidirect
4. #11736830C2direct (N × H)
5. C2×#89601C2semidirect
6. C2×#89621C2semidirect
7. C2×#89619C2semidirect
8. C2×#89613C2semidirect
11. C2×#89494C2semidirect
12. C2×#89493C2semidirect
13. C2×#89488C2semidirect
14. C2×#89482C2semidirect
15. C2×C4×Dic28C2semidirect
16. C2×C4×#1132C2semidirect
29. #90209C22semidirect
46. C7×#433C22semidirect
65. #89621C22semidirect
66. #89619C22semidirect
67. #89613C22semidirect
68. #89601C22semidirect
71. #89494C22semidirect
72. #89493C22semidirect
73. #89488C22semidirect
74. #89482C22semidirect
75. C4×Dic28C22semidirect
76. C4×#1132C22semidirect
198. C2×#433D7semidirect
335. #433C2×D7semidirect
643. C2×C7#3120semidirect
709. C7C2×#3120semidirect
739. C2#11736830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902142
C2×#902092
C2×C7×#4332
#117368302
C2×#896012
C2×#896212
C2×#896192
C2×#896132
C2×#895052
C2×#894942
C2×#894932
C2×#894882
C2×#894822
C2×C4×Dic282
C2×C4×#11322
C2×#31207