Finite Group Databasebeta

← C2×#11739000 #14230691

Subgroups — C2×#11739000 #14230691

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90323C211yesmaximal, characteristic, complemented
2C2×#90223C211yesmaximal, characteristic
3C2×C7×#485C211yesmaximal, characteristic, complemented
4C2×#89821C211yesmaximal, characteristic, complemented
5C2×#89776C211yesmaximal, characteristic, complemented
6#11739000C2116yesmaximal, direct product factor
7C2×#89647C211yesmaximal, characteristic, complemented
8C2×#89658C211yesmaximal, characteristic, complemented
9C2×#89639C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89590C211yesmaximal, characteristic, complemented
12C2×#89578C211yesmaximal, characteristic, complemented
13C2×#89574C211yesmaximal, characteristic, complemented
14C2×#89564C211yesmaximal, characteristic, complemented
15C2×#89510C211yesmaximal, characteristic, complemented
16C2×#89501C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C2×#6507C2211yescharacteristic
22C22×#1143C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×C4×C22⋊D7C2211yescharacteristic
25C22×#1136C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28C22×#1131C2211yescharacteristic
29#90323—24no—
30#90323C2218yescomplemented
31#90223—24no—
32#90223C2218yes—
33C2×#6460C2211yescharacteristic
34C2×#6459—21no—
35C2×#6458C2211yescharacteristic
36C2×#6456C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×#6451—21no—
39C2×#6451C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×#6448—21no—
42C2×#6447—21no—
43C2×(C22⋊D7)⋊C4—21no—
44C2×#6441—21no—
45C2×#6438—21no—
46C2×#6435—21no—
47C7×#485C2218yescomplemented
48C2×C7×#107C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52C2×C7×C22⋊C8C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89821C2218yescomplemented
60#89776C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89658C2218yescomplemented
68#89647C2218yescomplemented
69#89639C2218yescomplemented
70#89624C2218yescomplemented
71#89590C2218yescomplemented
72#89578C2218yescomplemented
73#89574C2218yescomplemented
74#89564C2218yescomplemented
75#89510C2218yescomplemented
76#89501C2218yescomplemented
77C2×#3329—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—21no—
81C22×C22⋊D7D411yescharacteristic
82C23×Dic7—21no—
83C2×Q8×D7—22no—
84C2×Q8×D7—24no—
85C2×Q8×D7—42no—
86C2×Q8×D7C2314yes—
87C22×D28—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—24no—
93C22×Dic14—21no—
94C22×Dic14—22no—
95C22×Dic14—21no—
96C22×Dic14—21no—
97C22×Dic14—42no—
98C22×Dic14C2311yescharacteristic
99C22×Dic14C2314yes—
100C22×Dic14C2311yescharacteristic
101C22×C7×C8C2311yescharacteristic
102C22×C7×C8C2311yescharacteristic
103C7×C22⋊Q8—22no—
104C7×C22⋊Q8C2314yes—
105C7×#117—22no—
106C7×#117C2314yes—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C42×C7—21no—
114C2×C22⋊Dic7D411yescharacteristic
115#6507—22no—
116#6507C2314yes—
117C2×#1143—42no—
118C2×#1143C2314yes—
119#6493—22no—
120#6493C2314yes—
121C4×C22⋊D7D414yes—
122C4×C22⋊D7C2314yes—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4D411yescharacteristic
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7C2311yescharacteristic
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4D411yescharacteristic
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7C2311yescharacteristic
139C2×#1136—42no—
140C2×#1136C2314yes—
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C2×#1132—24no—
144C2×#1132—42no—
145C2×#1132C2314yes—
146C2×#1132C2314yes—
147C2×#1131—42no—
148C2×#1131C2314yes—
149#6460—22no—
150#6460C2314yes—
151#6459—28no—
152#6458—22no—
153#6458C2314yes—
154#6456—22no—
155#6456C2314yes—
156#6455—22no—
157#6455C2314yes—
158#6451—28no—
159#6451—22no—
160#6451C2314yes—
161#6450—22no—
162#6450C2314yes—
163#6448—28no—
164#6447—28no—
165(C22⋊D7)⋊C4—28no—
166#6441—28no—
167#6438—28no—
168#6435—28no—
169C7×#107C2314yes—
170C7×#106C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173C7×C22⋊C8C2314yes—
174#6409C2314yes—
175(C2×D7)⋊C8C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178Dic7⋊C8C2314yes—
179C8×Dic7C2314yes—
180#6384C2314yes—
181#6384C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6383C2314yes—
185#6381C2314yes—
186C2×#555—71no—
187C2×D4×Q8—71no—
188#3329—716no—
189C2×#487—71no—
190C2×#485—71no—
191C2×#485D711yescharacteristic, complemented
192C2×#477—71no—
193C2×#468—71no—
194C2×#468—71no—
195C2×#461—71no—
196C2×#448—71no—
197C2×#448—71no—
198C2×C4×SD16—71no—
199C2×#436—71no—
200C2×#419—71no—
201C2×#419—71no—
202C24×C7C2×D411yescharacteristic
203C23×D7—21no—
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8C2412yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—82no—
222C2×C22⋊D7C2×D414yes—
223C22×Dic7—21no—
224C22×Dic7—24no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—44no—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231Q8×D7—28no—
232Q8×D7—44no—
233Q8×D7—48no—
234C2×D28—22no—
235C2×D28—22no—
236C2×D28—21no—
237C2×D28—24no—
238C2×D28—82no—
239C2×D28C2412yes—
240C2×C4×D7—22no—
241C2×C4×D7—22no—
242C2×C4×D7—24no—
243C2×C4×D7—24no—
244C2×C4×D7—44no—
245C2×C4×D7—44no—
246C2×C4×D7C2×D412yes—
247C2×C4×D7C2412yes—
248C2×Dic14—21no—
249C2×Dic14—22no—
250C2×Dic14—22no—
251C2×Dic14—22no—
252C2×Dic14—28no—
253C2×Dic14—24no—
254C2×Dic14—21no—
255C2×Dic14—24no—
256C2×Dic14—24no—
257C2×Dic14—44no—
258C2×Dic14—48no—
259C2×Dic14—44no—
260C2×Dic14—44no—
261C2×Dic14—82no—
262C2×Dic14#4114yes—
263C2×Dic14C2412yes—
264C2×Dic14C2412yes—
265C2×C7×C8—22no—
266C2×C7×C8—22no—
267C2×C7×C8C2412yes—
268C2×C7×C8C2412yes—
269C7×C4⋊C4—21no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—21no—
273C7×C4⋊C4C2412yes—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C22⋊C4—24no—
277C7×C22⋊C4—24no—
278C42×C7—24no—
279C22⋊Dic7C2×D414yes—
280#1143—44no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4C2×D414yes—
287C4⋊Dic7—21no—
288C4⋊Dic7—24no—
289C4⋊Dic7C2412yes—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293Dic7⋊C4—24no—
294Dic7⋊C4C2×D414yes—
295C4×Dic7—24no—
296C4×Dic7—24no—
297C4×Dic7C2×D412yes—
298C4×Dic7C2412yes—
299#1136—44no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8—22no—
302C2×C7⋊C8C2412yes—
303C2×C7⋊C8C2412yes—
304#1132—28no—
305#1132—44no—
306#1131—44no—
307C23×Q8—71no—
308C23×Q8—71no—
309C22×SD16—71no—
310C22×SD16—71no—
311C22×SD16—71no—
312C22×M16—71no—
313C22×M16—71no—
314#555—78no—
315#555—144no—
316D4×Q8—78no—
317D4×Q8—144no—
318C2×C4⋊Q8—71no—
319C2×C4⋊Q8—71no—
320C2×C4⋊Q8—141no—
321C2×#124—141no—
322C2×#124—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—141no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×#121—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×C4×Q8—71no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×#117—71no—
335C2×#117—141no—
336C2×#117C2×D711yescharacteristic
337#487—78no—
338#485—78no—
339#485C2×D718yescomplemented
340#477—78no—
341#468—78no—
342#468—78no—
343#461—78no—
344#448—78no—
345#448—78no—
346C4×SD16—78no—
347#436—78no—
348C2×#107—71no—
349C2×#107C2×D711yescharacteristic
350C2×#106C2×D711yescharacteristic
351C2×C4⋊C8—71no—
352#419—78no—
353#419—78no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103—71no—
361C2×#103C2×D711yescharacteristic
362C2×#103C2×D711yescharacteristic
363C2×#102—71no—
364C2×C22⋊C8—71no—
365C2×C22⋊C8C2×D711yescharacteristic
366C2×C4×C8—71no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7C22×D412yes—
371C23×C7C22×D411yescharacteristic
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—42no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7C22×D412yes—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—42no—
383C2×C4×C7—22no—
384C2×C4×C7—24no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7C2×#4112yes—
398C2×C4×C7H(5,𝔽2)12yes—
399C2×C4×C7C2511yescharacteristic
400C22⋊D7—28no—
401C22⋊D7—84no—
402C2×Dic7—24no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—48no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7#13714yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415D28—22no—
416D28—22no—
417D28—42no—
418D28—84no—
419C4×D7—24no—
420C4×D7—22no—
421C4×D7—22no—
422C4×D7—48no—
423C4×D7—48no—
424Dic14—24no—
425Dic14—22no—
426Dic14—22no—
427Dic14—22no—
428Dic14—48no—
429Dic14—48no—
430Dic14—42no—
431Dic14—84no—
432Dic14C2×#4114yes—
433C7×C8—22no—
434C7×C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C22×Q8—74no—
438C22×Q8—71no—
439C22×Q8—71no—
440C22×Q8—74no—
441C22×Q8—141no—
442C22×Q8—141no—
443C22×Q8—144no—
444C22×Q8—142no—
445C22×Q8—141no—
446C22×Q8—142no—
447C22×Q8—144no—
448C22×Q8—282no—
449C22×Q8—282no—
450C22×Q8C22×D711yescharacteristic
451C22×D4—71no—
452C22×D4—71no—
453C22×D4—141no—
454C22×D4—141no—
455C23×C4—71no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4—141no—
459C23×C4C22×D711yescharacteristic
460C2×SD16—74no—
461C2×SD16—74no—
462C2×SD16—74no—
463C2×SD16—144no—
464C2×SD16—282no—
465C2×SD16—282no—
466C2×M16—74no—
467C2×M16—74no—
468C2×M16—282no—
469C2×M16—282no—
470C22×C8—71no—
471C22×C8—71no—
472C22×C8C22×D711yescharacteristic
473C22×C8C22×D711yescharacteristic
474C4⋊Q8—74no—
475C4⋊Q8—74no—
476C4⋊Q8—142no—
477C4⋊Q8—142no—
478C4⋊Q8—148no—
479#124—148no—
480#124—148no—
481C22⋊Q8—22no—
482C22⋊Q8—74no—
483C22⋊Q8—148no—
484C22⋊Q8—148no—
485C22⋊Q8—142no—
486C22⋊Q8C22×D714yes—
487#121—74no—
488#121—74no—
489#121—148no—
490#121—142no—
491#121—142no—
492C4×Q8—74no—
493C4×Q8—142no—
494C4×D4—74no—
495C4×D4—74no—
496C4×D4—74no—
497C4×D4—142no—
498C4×D4—148no—
499#117—22no—
500#117—74no—
501#117—148no—
502#117—142no—
503#117C22×D714yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4C22×D711yescharacteristic
513C2×C4⋊C4C22×D711yescharacteristic
514C2×C4⋊C4C22×D711yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—71no—
518C2×C22⋊C4—71no—
519C2×C22⋊C4—141no—
520C2×C22⋊C4—141no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4—141no—
524C2×C42—21no—
525C2×C42—71no—
526C2×C42—141no—
527C2×C42—141no—
528#107—74no—
529#107C22×D714yes—
530#106C22×D714yes—
531C4⋊C8—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103C22×D714yes—
540#103C22×D714yes—
541#102—74no—
542C22⋊C8—74no—
543C22⋊C8C22×D714yes—
544C4×C8—74no—
545C22×C7—22no—
546C22×C7—22no—
547C22×C7—22no—
548C22×C7—44no—
549C22×C7#54612yes—
550C22×C7C2×#13712yes—
551C22×C7#57712yes—
552C22×C7C23×D411yescharacteristic
553C2×D7—22no—
554C2×D7—22no—
555C2×D7—22no—
556C2×D7—44no—
557C2×D7—42no—
558C2×D7—42no—
559C2×D7—42no—
560C2×D7—84no—
561C4×C7—22no—
562C4×C7—42no—
563C4×C7—42no—
564C4×C7—42no—
565C4×C7—42no—
566C4×C7#54612yes—
567C4×C7C22×#4111yescharacteristic
568C4×C7C2×H(5,𝔽2)11yescharacteristic
569Dic7—24no—
570Dic7—22no—
571Dic7—22no—
572Dic7—42no—
573Dic7—42no—
574Dic7C2×#13714yes—
575C24—71no—
576C24—141no—
577C24D4×D711yescharacteristic
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—74no—
582C2×Q8—72no—
583C2×Q8—72no—
584C2×Q8—144no—
585C2×Q8—144no—
586C2×Q8—148no—
587C2×Q8—141no—
588C2×Q8—144no—
589C2×Q8—141no—
590C2×Q8—142no—
591C2×Q8—148no—
592C2×Q8—142no—
593C2×Q8—142no—
594C2×Q8—284no—
595C2×Q8—284no—
596C2×Q8—288no—
597C2×Q8—284no—
598C2×Q8—284no—
599C2×Q8—288no—
600C2×Q8—562no—
601C2×Q8C23×D712yes—
602C2×D4—74no—
603C2×D4—72no—
604C2×D4—144no—
605C2×D4—144no—
606C2×D4—144no—
607C2×D4—141no—
608C2×D4—142no—
609C2×D4—142no—
610C2×D4—562no—
611C2×D4—562no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—71no—
619C22×C4—71no—
620C22×C4—71no—
621C22×C4—72no—
622C22×C4—72no—
623C22×C4—144no—
624C22×C4—144no—
625C22×C4—141no—
626C22×C4—142no—
627C22×C4—142no—
628C22×C4—144no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—284no—
632C22×C4—284no—
633C22×C4—284no—
634C22×C4D4×D712yes—
635C22×C4D4×D711yescharacteristic
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638SD16—148no—
639SD16—284no—
640SD16—284no—
641M16—284no—
642M16—284no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—72no—
646C2×C8—72no—
647C2×C8—142no—
648C2×C8—142no—
649C2×C8C23×D712yes—
650C2×C8C23×D712yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—74no—
656C4⋊C4—72no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4—144no—
662C4⋊C4—141no—
663C4⋊C4C23×D712yes—
664C4⋊C4C23×D712yes—
665C4⋊C4C23×D712yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—74no—
669C22⋊C4—74no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C22⋊C4—144no—
673C22⋊C4—144no—
674C22⋊C4—144no—
675C42—24no—
676C42—72no—
677C42—72no—
678C42—144no—
679C42—144no—
680C2×C7—42no—
681C2×C7#332914yescomplemented
682C2×C7C2×#54611yescharacteristic
683C2×C7C22×#13711yescharacteristic
684C2×C7C2×#57711yescharacteristic
685D7—42no—
686D7—82no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—72no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23—142no—
695C23—282no—
696C23—282no—
697C23—282no—
698C23C2×D4×D712yes—
699C23C2×D4×D711yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—42no—
703Q8—74no—
704Q8—144no—
705Q8—142no—
706Q8—142no—
707Q8—142no—
708Q8—288no—
709Q8—288no—
710Q8—282no—
711Q8—564no—
712D4—148no—
713D4—142no—
714D4—142no—
715D4—282no—
716D4—564no—
717D4—564no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—74no—
731C2×C4—72no—
732C2×C4—72no—
733C2×C4—72no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—144no—
737C2×C4—142no—
738C2×C4—144no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—288no—
744C2×C4—288no—
745C2×C4—288no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4C2×D4×D712yes—
749C2×C4C2×D4×D711yescharacteristic
750C2×C4D7×#4112yes—
751C2×C4#655312yes—
752C2×C4C24×D711yescharacteristic
753C8—22no—
754C8—22no—
755C8—142no—
756C8—142no—
757C7C2×#332911yescharacteristic, complemented, Sylow
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—142no—
763C22—142no—
764C22—142no—
765C22—284no—
766C22—282no—
767C22—282no—
768C22—282no—
769C22—564no—
770C22#9034512yes—
771C22#9046112yes—
772C22D7×#13712yes—
773C22C22×D4×D711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—74no—
780C4—142no—
781C4—144no—
782C4—142no—
783C4—282no—
784C4—282no—
785C4#9034512yes—
786C4C2×D7×#4111yescharacteristic
787C4C2×#655311yescharacteristic
788C2—42no—
789C2—282no—
790C2—562no—
791C2#1173900014yesdirect product factor
792C2C2×#9034511yescharacteristic
793C2C2×#9046111yescharacteristic
794C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#485C2
socleC23×C7C22×D4
prime radicalC2×#90223C2
hypercenterC2×#485D7
hypocenterC7C2×#3329
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#90323C2semidirect
3. C2×C7×#485C2semidirect
4. C2×#89821C2semidirect
5. C2×#89776C2semidirect
6. #11739000C2direct (N × H)
7. C2×#89647C2semidirect
8. C2×#89658C2semidirect
9. C2×#89639C2semidirect
10. C2×#89624C2semidirect
11. C2×#89590C2semidirect
12. C2×#89578C2semidirect
13. C2×#89574C2semidirect
14. C2×#89564C2semidirect
15. C2×#89510C2semidirect
16. C2×#89501C2semidirect
30. #90323C22semidirect
47. C7×#485C22semidirect
59. #89821C22semidirect
60. #89776C22semidirect
67. #89658C22semidirect
68. #89647C22semidirect
69. #89639C22semidirect
70. #89624C22semidirect
71. #89590C22semidirect
72. #89578C22semidirect
73. #89574C22semidirect
74. #89564C22semidirect
75. #89510C22semidirect
76. #89501C22semidirect
191. C2×#485D7semidirect
339. #485C2×D7semidirect
681. C2×C7#3329semidirect
757. C7C2×#3329semidirect
791. C2#11739000direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903232
C2×#902232
C2×C7×#4852
C2×#898212
C2×#897762
#117390002
C2×#896472
C2×#896582
C2×#896392
C2×#896242
C2×#895902
C2×#895782
C2×#895742
C2×#895642
C2×#895102
C2×#895012
C2×#33297