Finite Group Databasebeta

← C2×#11737665 #14225004

Subgroups — C2×#11737665 #14225004

Order 1792.

2186 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90523C211yesmaximal, characteristic
2C2×#90313C211yesmaximal, characteristic, complemented
3C2×C7×#452C211yesmaximal, characteristic, complemented
4C2×#90011C211yesmaximal, characteristic, complemented
5C2×#89953C211yesmaximal, characteristic, complemented
6C2×#89957C211yesmaximal, characteristic, complemented
7C2×#89947C211yesmaximal, characteristic, complemented
8C2×#89938C211yesmaximal, characteristic, complemented
9C2×#89819C211yesmaximal, characteristic, complemented
10#11737665C2116yesmaximal, direct product factor
11C2×#89570C211yesmaximal, characteristic, complemented
12C2×#89564C211yesmaximal, characteristic, complemented
13C2×#89539C211yesmaximal, characteristic, complemented
14C2×#89532C211yesmaximal, characteristic, complemented
15C2×#89505C211yesmaximal, characteristic, complemented
16C2×#89490C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22#90523—24no—
23#90523C2218yes—
24C2×#6510C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×#6507C2211yescharacteristic
27C2×#6507C2211yescharacteristic
28C22×#1144C2211yescharacteristic
29C22×#1144C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C2×#6503C2211yescharacteristic
32C2×#6502—21no—
33C2×#6502—21no—
34C2×#6499C2211yescharacteristic
35C22×#1142C2211yescharacteristic
36C2×C4×C22⋊D7—21no—
37C2×C4×C22⋊D7—21no—
38C2×#6487C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×Dic28C2211yescharacteristic
41C22×#1132C2211yescharacteristic
42#90313—24no—
43#90313C2218yescomplemented
44C2×#6452—21no—
45C2×#6451C2211yescharacteristic
46C2×#6450—21no—
47C2×#6450C2211yescharacteristic
48C2×#6441—21no—
49C2×#6440—21no—
50C7×#452C2218yescomplemented
51C2×C7×#103C2211yescharacteristic
52C2×C7×#102C2211yescharacteristic
53C2×C7×C22⋊C8C2211yescharacteristic
54#90011C2218yescomplemented
55C2×#6409C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57C2×C22⋊(C7⋊C8)C2211yescharacteristic
58#89957C2218yescomplemented
59#89953C2218yescomplemented
60#89947C2218yescomplemented
61#89938C2218yescomplemented
62C2×#6395C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66C2×C8×Dic7C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89819C2218yescomplemented
69C2×#6384C2211yescharacteristic
70C2×#6383C2211yescharacteristic
71#89570C2218yescomplemented
72#89564C2218yescomplemented
73#89539C2218yescomplemented
74#89532C2218yescomplemented
75#89505C2218yescomplemented
76#89490C2218yescomplemented
77C2×#3210—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—42no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2311yescharacteristic
84C22×C7×D4—21no—
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—21no—
89C22×C22⋊D7—21no—
90C22×C22⋊D7—21no—
91C23×Dic7D411yescharacteristic
92C23×Dic7D411yescharacteristic
93C2×#1157—22no—
94C2×#1157—42no—
95C2×#1157—42no—
96C2×#1157C2314yes—
97C22×D28C2311yescharacteristic
98C22×C4×D7—21no—
99C22×Dic14—21no—
100C22×Dic14C2311yescharacteristic
101C22×Dic14C2311yescharacteristic
102C2×C7×Q16—42no—
103C2×C7×Q16C2314yes—
104C2×C7×SD16—42no—
105C2×C7×SD16C2314yes—
106C22×C7×C8C2311yescharacteristic
107C22×C7×C8C2311yescharacteristic
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116#6510—22no—
117#6510C2314yes—
118Q8×Dic7—22no—
119Q8×Dic7C2314yes—
120#6507—22no—
121#6507—22no—
122#6507C2314yes—
123#6507C2314yes—
124C2×#1144—42no—
125C2×#1144—42no—
126C2×#1144C2314yes—
127C2×#1144C2314yes—
128C2×#1143—42no—
129C2×#1143C2314yes—
130#6503—22no—
131#6503C2314yes—
132#6502—28no—
133#6502—28no—
134#6499—22no—
135#6499C2314yes—
136C2×#1142—42no—
137C2×#1142C2314yes—
138C4×C22⋊D7—28no—
139C4×C22⋊D7—28no—
140C2×(C2×D7)⋊C4—21no—
141C2×(C2×D7)⋊C4—21no—
142C2×C4⋊Dic7—21no—
143C2×C4⋊Dic7C2311yescharacteristic
144#6487—22no—
145#6487C2314yes—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4—21no—
153C2×C4×Dic7—21no—
154C2×C4×Dic7—21no—
155C2×C4×Dic7D411yescharacteristic
156C2×C4×Dic7D411yescharacteristic
157C2×C4×Dic7D414yes—
158C2×C4×Dic7C2311yescharacteristic
159C2×C4×Dic7C2311yescharacteristic
160C2×C4×Dic7C2314yes—
161C22×C7⋊C8C2311yescharacteristic
162C22×C7⋊C8C2311yescharacteristic
163C2×Dic28—42no—
164C2×Dic28C2314yes—
165C2×#1132—42no—
166C2×#1132C2314yes—
167#6452—28no—
168#6451—22no—
169#6451C2314yes—
170#6450—28no—
171#6450—22no—
172#6450C2314yes—
173#6441—28no—
174#6440—28no—
175C7×#103C2314yes—
176C7×#102C2314yes—
177C7×C22⋊C8C2314yes—
178#6409C2314yes—
179#6406C2314yes—
180C22⋊(C7⋊C8)C2314yes—
181#6395C2314yes—
182#6390C2314yes—
183Dic7⋊C8C2314yes—
184Dic7⋊C8C2314yes—
185C8×Dic7C2314yes—
186C8×Dic7C2314yes—
187#6384C2314yes—
188#6383C2314yes—
189C2×#533—71no—
190C2×#532—71no—
191#3210—716no—
192C2×#494—71no—
193C2×#492—71no—
194C2×#487—71no—
195C2×#486—71no—
196C2×#464—71no—
197C2×#464—71no—
198C2×#464—71no—
199C2×#464—71no—
200C2×#452—71no—
201C2×#452—71no—
202C2×#452—71no—
203C2×#452D711yescharacteristic, complemented
204C2×#431—71no—
205C24×C7—21no—
206C24×C7C2×D411yescharacteristic
207C23×D7—21no—
208C7×#41—44no—
209C7×#41—44no—
210C7×#41—48no—
211C2×C7×Q8—21no—
212C2×C7×Q8—21no—
213C2×C7×Q8—22no—
214C2×C7×Q8—22no—
215C2×C7×Q8—22no—
216C2×C7×Q8—22no—
217C2×C7×Q8C2412yes—
218C2×C7×Q8C2412yes—
219C2×C7×D4—24no—
220C2×C7×D4—21no—
221C2×C7×D4—22no—
222C2×C7×D4—22no—
223C2×C7×D4—44no—
224C2×C7×D4C2412yes—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—24no—
231C22×C4×C7—44no—
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2411yescharacteristic
236C2×C22⋊D7—24no—
237C2×C22⋊D7—24no—
238C2×C22⋊D7—24no—
239C2×C22⋊D7—44no—
240C2×C22⋊D7—44no—
241C2×C22⋊D7—44no—
242C22×Dic7—24no—
243C22×Dic7—24no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7C2×D414yes—
248C22×Dic7C2×D414yes—
249C22×Dic7C2×D411yescharacteristic
250C22×Dic7C2×D411yescharacteristic
251C22×Dic7C2×D411yescharacteristic
252C22×Dic7C2×D411yescharacteristic
253#1157—44no—
254#1157—44no—
255#1157—48no—
256C2×D28—22no—
257C2×D28—22no—
258C2×D28—21no—
259C2×D28C2412yes—
260C2×C4×D7—24no—
261C2×C4×D7—44no—
262C2×Dic14—22no—
263C2×Dic14—22no—
264C2×Dic14—22no—
265C2×Dic14—22no—
266C2×Dic14—21no—
267C2×Dic14—21no—
268C2×Dic14—24no—
269C2×Dic14—44no—
270C2×Dic14C2412yes—
271C2×Dic14C2412yes—
272C7×Q16—44no—
273C7×SD16—44no—
274C2×C7×C8—22no—
275C2×C7×C8—22no—
276C2×C7×C8C2412yes—
277C2×C7×C8C2412yes—
278C7×C4⋊C4—21no—
279C7×C4⋊C4—24no—
280C7×C4⋊C4C2412yes—
281C7×C22⋊C4—24no—
282C22⋊Dic7—24no—
283C22⋊Dic7—24no—
284C22⋊Dic7—24no—
285#1144—44no—
286#1144—44no—
287#1143—44no—
288#1142—44no—
289(C2×D7)⋊C4—24no—
290(C2×D7)⋊C4—24no—
291C4⋊Dic7—21no—
292C4⋊Dic7—24no—
293C4⋊Dic7C2412yes—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298Dic7⋊C4—24no—
299Dic7⋊C4—24no—
300Dic7⋊C4—24no—
301C4×Dic7—24no—
302C4×Dic7—24no—
303C4×Dic7C2×D414yes—
304C4×Dic7C2×D412yes—
305C4×Dic7C2×D412yes—
306C4×Dic7C2×D414yes—
307C4×Dic7C2412yes—
308C4×Dic7C2412yes—
309C2×C7⋊C8—22no—
310C2×C7⋊C8—22no—
311C2×C7⋊C8C2412yes—
312C2×C7⋊C8C2412yes—
313Dic28—44no—
314#1132—44no—
315C22×#41—71no—
316C22×#41C2×D711yescharacteristic
317C22×Q16—71no—
318C22×Q16—71no—
319C22×Q16—71no—
320C22×Q16C2×D711yescharacteristic
321C22×SD16—71no—
322C22×SD16—71no—
323C22×SD16—71no—
324C22×SD16C2×D711yescharacteristic
325#533—78no—
326#533—144no—
327#532—78no—
328#532—144no—
329C2×C4⋊Q8—71no—
330C2×C4⋊Q8—71no—
331C2×C4⋊Q8—71no—
332C2×#127—71no—
333C2×#125—141no—
334C2×#124—71no—
335C2×#124—71no—
336C2×C22⋊Q8—71no—
337C2×C22⋊Q8—141no—
338C2×C22⋊Q8C2×D711yescharacteristic
339C2×#121—141no—
340C2×#121—141no—
341C2×C4×Q8—71no—
342C2×C4×Q8—71no—
343C2×C4×Q8—141no—
344C2×C4×D4—141no—
345C2×C4×D4—141no—
346C2×#117—141no—
347C22×C42—71no—
348#494—78no—
349#492—78no—
350#487—78no—
351#486—78no—
352#464—78no—
353#464—78no—
354#464—78no—
355#464—78no—
356#452—78no—
357#452—78no—
358#452—78no—
359#452C2×D718yescomplemented
360#431—78no—
361C2×C4⋊C8—71no—
362C2×C4⋊C8—71no—
363C2×#103—71no—
364C2×#103—71no—
365C2×#103—71no—
366C2×#103C2×D711yescharacteristic
367C2×#102—71no—
368C2×#102—71no—
369C2×#102—71no—
370C2×#102C2×D711yescharacteristic
371C2×C22⋊C8—71no—
372C2×C22⋊C8C2×D711yescharacteristic
373C2×C4×C8—71no—
374C2×C4×C8—71no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7—42no—
382C23×C7C22×D412yes—
383C23×C7C22×D411yescharacteristic
384C22×D7—22no—
385C22×D7—42no—
386C22×D7—42no—
387C22×D7—42no—
388C7×Q8—22no—
389C7×Q8—22no—
390C7×Q8—22no—
391C7×Q8—22no—
392C7×Q8—42no—
393C7×Q8—42no—
394C7×D4—22no—
395C7×D4—22no—
396C7×D4—48no—
397C7×D4—42no—
398C2×C4×C7—22no—
399C2×C4×C7—24no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—48no—
406C2×C4×C7—42no—
407C2×C4×C7—42no—
408C2×C4×C7—42no—
409C2×C4×C7C22×D412yes—
410C2×C4×C7C22×D411yescharacteristic
411C2×C4×C7H(5,𝔽2)12yes—
412C2×C4×C7H(5,𝔽2)12yes—
413C2×C4×C7C2511yescharacteristic
414C22⋊D7—48no—
415C22⋊D7—48no—
416C22⋊D7—48no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—28no—
420C2×Dic7—28no—
421C2×Dic7—22no—
422C2×Dic7—22no—
423C2×Dic7—22no—
424C2×Dic7—42no—
425C2×Dic7—42no—
426C2×Dic7—42no—
427C2×Dic7#13514yes—
428C2×Dic7#13714yes—
429C2×Dic7C22×D412yes—
430C2×Dic7C22×D412yes—
431C2×Dic7C22×D412yes—
432C2×Dic7C22×D412yes—
433D28—22no—
434D28—22no—
435D28—42no—
436C4×D7—48no—
437Dic14—22no—
438Dic14—22no—
439Dic14—22no—
440Dic14—22no—
441Dic14—42no—
442Dic14—42no—
443Dic14—48no—
444C7×C8—22no—
445C7×C8—22no—
446C7⋊C8—22no—
447C7⋊C8—22no—
448C2×#41—22no—
449C2×#41—42no—
450C2×#41—42no—
451C2×#41—74no—
452C2×#41—142no—
453C2×#41—282no—
454C2×#41—282no—
455C2×#41C22×D714yes—
456C22×Q8—71no—
457C22×Q8—71no—
458C22×Q8—141no—
459C22×Q8C22×D711yescharacteristic
460C22×Q8C22×D711yescharacteristic
461C22×D4—21no—
462C22×D4—71no—
463C22×D4—141no—
464C22×D4—141no—
465C22×D4—141no—
466C22×D4C22×D711yescharacteristic
467C23×C4—21no—
468C23×C4—71no—
469C23×C4—71no—
470C23×C4—141no—
471C23×C4C22×D711yescharacteristic
472C2×Q16—42no—
473C2×Q16—74no—
474C2×Q16—74no—
475C2×Q16—74no—
476C2×Q16—282no—
477C2×Q16—282no—
478C2×Q16—282no—
479C2×Q16C22×D714yes—
480C2×SD16—42no—
481C2×SD16—74no—
482C2×SD16—74no—
483C2×SD16—74no—
484C2×SD16—282no—
485C2×SD16—282no—
486C2×SD16—282no—
487C2×SD16C22×D714yes—
488C22×C8—71no—
489C22×C8—71no—
490C22×C8C22×D711yescharacteristic
491C22×C8C22×D711yescharacteristic
492C4⋊Q8—74no—
493C4⋊Q8—74no—
494C4⋊Q8—74no—
495C4⋊Q8—142no—
496C4⋊Q8—142no—
497C4⋊Q8—142no—
498#127—74no—
499#127—142no—
500#125—148no—
501#124—74no—
502#124—74no—
503#124—142no—
504#124—142no—
505C22⋊Q8—22no—
506C22⋊Q8—74no—
507C22⋊Q8—148no—
508C22⋊Q8—142no—
509C22⋊Q8C22×D714yes—
510#121—148no—
511#121—148no—
512C4×Q8—74no—
513C4×Q8—74no—
514C4×Q8—142no—
515C4×Q8—148no—
516C4×Q8—142no—
517C4×D4—148no—
518C4×D4—148no—
519#117—148no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—71no—
522C2×C4⋊C4—141no—
523C2×C4⋊C4—141no—
524C2×C4⋊C4—141no—
525C2×C4⋊C4—141no—
526C2×C4⋊C4—141no—
527C2×C4⋊C4—141no—
528C2×C4⋊C4—141no—
529C2×C4⋊C4—141no—
530C2×C4⋊C4C22×D711yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—141no—
533C2×C22⋊C4—141no—
534C2×C22⋊C4—141no—
535C2×C22⋊C4—141no—
536C2×C22⋊C4—141no—
537C2×C42—71no—
538C2×C42—71no—
539C2×C42—74no—
540C2×C42—71no—
541C2×C42—71no—
542C2×C42—74no—
543C2×C42—141no—
544C2×C42—141no—
545C4⋊C8—74no—
546C4⋊C8—74no—
547#103—74no—
548#103—74no—
549#103—74no—
550#103C22×D714yes—
551#102—74no—
552#102—74no—
553#102—74no—
554#102C22×D714yes—
555C22⋊C8—74no—
556C22⋊C8C22×D714yes—
557C4×C8—74no—
558C4×C8—74no—
559C22×C7—22no—
560C22×C7—22no—
561C22×C7—22no—
562C22×C7—44no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—84no—
567C22×C7#53512yes—
568C22×C7C2×#13512yes—
569C22×C7C2×#13712yes—
570C22×C7C23×D411yescharacteristic
571C2×D7—42no—
572C2×D7—42no—
573C2×D7—42no—
574C2×D7—84no—
575C4×C7—22no—
576C4×C7—42no—
577C4×C7—42no—
578C4×C7—42no—
579C4×C7#53512yes—
580C4×C7C2×H(5,𝔽2)11yescharacteristic
581C4×C7C2×H(5,𝔽2)11yescharacteristic
582Dic7—22no—
583Dic7—22no—
584Dic7—42no—
585Dic7—42no—
586Dic7—42no—
587Dic7C2×#13514yes—
588Dic7C2×#13714yes—
589C24—21no—
590C24—141no—
591C24D4×D711yescharacteristic
592#41—44no—
593#41—44no—
594#41—48no—
595#41—284no—
596#41—284no—
597#41—288no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—72no—
605C2×Q8—72no—
606C2×Q8—144no—
607C2×Q8—141no—
608C2×Q8—141no—
609C2×Q8—142no—
610C2×Q8—142no—
611C2×Q8—142no—
612C2×Q8—142no—
613C2×Q8—284no—
614C2×Q8C23×D712yes—
615C2×Q8C23×D712yes—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—72no—
622C2×D4—144no—
623C2×D4—144no—
624C2×D4—144no—
625C2×D4—141no—
626C2×D4—142no—
627C2×D4—142no—
628C2×D4—284no—
629C2×D4—284no—
630C2×D4—284no—
631C2×D4C23×D712yes—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—71no—
640C22×C4—71no—
641C22×C4—74no—
642C22×C4—74no—
643C22×C4—71no—
644C22×C4—71no—
645C22×C4—144no—
646C22×C4—144no—
647C22×C4—141no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—144no—
651C22×C4—284no—
652C22×C4D4×D712yes—
653C22×C4D4×D711yescharacteristic
654C22×C4C23×D712yes—
655C22×C4C23×D711yescharacteristic
656Q16—44no—
657Q16—284no—
658Q16—284no—
659Q16—284no—
660SD16—44no—
661SD16—284no—
662SD16—284no—
663SD16—284no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—72no—
667C2×C8—72no—
668C2×C8—142no—
669C2×C8—142no—
670C2×C8C23×D712yes—
671C2×C8C23×D712yes—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—72no—
675C4⋊C4—144no—
676C4⋊C4—144no—
677C4⋊C4—144no—
678C4⋊C4—144no—
679C4⋊C4—144no—
680C4⋊C4—144no—
681C4⋊C4—144no—
682C4⋊C4—144no—
683C4⋊C4—141no—
684C4⋊C4C23×D712yes—
685C22⋊C4—24no—
686C22⋊C4—144no—
687C22⋊C4—144no—
688C22⋊C4—144no—
689C22⋊C4—144no—
690C22⋊C4—144no—
691C42—74no—
692C42—74no—
693C42—72no—
694C42—72no—
695C42—72no—
696C42—72no—
697C42—144no—
698C42—144no—
699C2×C7—42no—
700C2×C7—82no—
701C2×C7#321014yescomplemented
702C2×C7C2×#53511yescharacteristic
703C2×C7C22×#13511yescharacteristic
704C2×C7C22×#13711yescharacteristic
705D7—82no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—142no—
714C23—282no—
715C23—282no—
716C23—282no—
717C23C2×D4×D712yes—
718C23C2×D4×D711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—42no—
724Q8—42no—
725Q8—142no—
726Q8—142no—
727Q8—142no—
728Q8—142no—
729Q8—288no—
730Q8—282no—
731Q8—282no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—142no—
737D4—142no—
738D4—288no—
739D4—288no—
740D4—288no—
741D4—282no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—74no—
754C2×C4—74no—
755C2×C4—72no—
756C2×C4—72no—
757C2×C4—72no—
758C2×C4—72no—
759C2×C4—148no—
760C2×C4—148no—
761C2×C4—142no—
762C2×C4—142no—
763C2×C4—142no—
764C2×C4—142no—
765C2×C4—142no—
766C2×C4—288no—
767C2×C4—282no—
768C2×C4—282no—
769C2×C4—282no—
770C2×C4C2×D4×D712yes—
771C2×C4C2×D4×D711yescharacteristic
772C2×C4#654812yes—
773C2×C4#654812yes—
774C2×C4C24×D711yescharacteristic
775C8—22no—
776C8—22no—
777C8—142no—
778C8—142no—
779C7C2×#321011yescharacteristic, complemented, Sylow
780C22—22no—
781C22—22no—
782C22—22no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22—282no—
789C22—282no—
790C22—282no—
791C22—564no—
792C22#9028312yes—
793C22D7×#13512yes—
794C22D7×#13712yes—
795C22C22×D4×D711yescharacteristic
796C4—22no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—74no—
801C4—74no—
802C4—142no—
803C4—142no—
804C4—282no—
805C4—282no—
806C4—282no—
807C4#9028312yes—
808C4C2×#654811yescharacteristic
809C4C2×#654811yescharacteristic
810C2—42no—
811C2—82no—
812C2—562no—
813C2#1173766514yesdirect product factor
814C2C2×#9028311yescharacteristic
815C2C2×D7×#13511yescharacteristic
816C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#452C2
socleC23×C7C22×D4
prime radicalC2×#90523C2
hypercenterC2×#452D7
hypocenterC7C2×#3210
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×#90313C2semidirect
3. C2×C7×#452C2semidirect
4. C2×#90011C2semidirect
5. C2×#89953C2semidirect
6. C2×#89957C2semidirect
7. C2×#89947C2semidirect
8. C2×#89938C2semidirect
9. C2×#89819C2semidirect
10. #11737665C2direct (N × H)
11. C2×#89570C2semidirect
12. C2×#89564C2semidirect
13. C2×#89539C2semidirect
14. C2×#89532C2semidirect
15. C2×#89505C2semidirect
16. C2×#89490C2semidirect
43. #90313C22semidirect
50. C7×#452C22semidirect
54. #90011C22semidirect
58. #89957C22semidirect
59. #89953C22semidirect
60. #89947C22semidirect
61. #89938C22semidirect
68. #89819C22semidirect
71. #89570C22semidirect
72. #89564C22semidirect
73. #89539C22semidirect
74. #89532C22semidirect
75. #89505C22semidirect
76. #89490C22semidirect
203. C2×#452D7semidirect
359. #452C2×D7semidirect
701. C2×C7#3210semidirect
779. C7C2×#3210semidirect
813. C2#11737665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905232
C2×#903132
C2×C7×#4522
C2×#900112
C2×#899532
C2×#899572
C2×#899472
C2×#899382
C2×#898192
#117376652
C2×#895702
C2×#895642
C2×#895392
C2×#895322
C2×#895052
C2×#894902
C2×#32107