Finite Group Databasebeta

← C2×#11736418 #14230689

Subgroups — C2×#11736418 #14230689

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×Q8×C22⋊D7C211yesmaximal, characteristic, complemented
2C2×#90223C211yesmaximal, characteristic
3C2×C7×#419C211yesmaximal, characteristic, complemented
4C2×#89999C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic, complemented
6C2×#89900C211yesmaximal, characteristic, complemented
7C2×#89768C211yesmaximal, characteristic, complemented
8#11736418C2116yesmaximal, direct product factor
9C2×#89590C211yesmaximal, characteristic, complemented
10C2×#89584C211yesmaximal, characteristic, complemented
11C2×#89578C211yesmaximal, characteristic, complemented
12C2×#89574C211yesmaximal, characteristic, complemented
13C2×#89564C211yesmaximal, characteristic, complemented
14C2×#89586C211yesmaximal, characteristic, complemented
15C2×#89566C211yesmaximal, characteristic, complemented
16C2×#89560C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×Q8×D7C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21Q8×C22⋊D7—24no—
22Q8×C22⋊D7C2218yescomplemented
23C2×#6509—21no—
24C2×#6509C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×#6507—21no—
27C2×#6507C2211yescharacteristic
28C22×#1143C2211yescharacteristic
29C22×#1143C2211yescharacteristic
30C2×#6493C2211yescharacteristic
31C2×C4×C22⋊D7—21no—
32C2×C4×C22⋊D7C2211yescharacteristic
33C2×#6487—21no—
34C2×#6487C2211yescharacteristic
35C22×#1132C2211yescharacteristic
36C22×#1131C2211yescharacteristic
37#90223—24no—
38#90223C2218yes—
39C2×#6458C2211yescharacteristic
40C2×#6456C2211yescharacteristic
41C2×#6455C2211yescharacteristic
42C2×#6451C2211yescharacteristic
43C2×#6448—21no—
44C2×#6447—21no—
45C2×#6438—21no—
46C2×#6435—21no—
47C7×#419C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52#89999C2218yescomplemented
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89906C2218yescomplemented
57#89900C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×(C2×D7)⋊C8C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×C8×Dic7C2211yescharacteristic
64#89768C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89590C2218yescomplemented
70#89586C2218yescomplemented
71#89584C2218yescomplemented
72#89578C2218yescomplemented
73#89574C2218yescomplemented
74#89566C2218yescomplemented
75#89564C2218yescomplemented
76#89560C2218yescomplemented
77C2×#3329—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—22no—
80C22×C7×Q8—24no—
81C22×C7×Q8—42no—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×Q8C2314yes—
84C22×C7×Q8C2311yescharacteristic
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—21no—
88C22×C22⋊D7D411yescharacteristic
89C2×Q8×D7—22no—
90C2×Q8×D7—24no—
91C2×Q8×D7—42no—
92C2×Q8×D7C2314yes—
93C22×D28—21no—
94C22×D28C2311yescharacteristic
95C22×C4×D7—21no—
96C22×C4×D7—21no—
97C22×C4×D7C2311yescharacteristic
98C22×Dic14—21no—
99C22×Dic14—21no—
100C22×Dic14C2311yescharacteristic
101C2×C7×M16—42no—
102C2×C7×M16C2314yes—
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C7×#117—22no—
106C7×#117C2314yes—
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C42×C7—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7D411yescharacteristic
113#6509—22no—
114#6509—28no—
115#6509C2314yes—
116Q8×Dic7—22no—
117Q8×Dic7C2314yes—
118#6507—28no—
119#6507—22no—
120#6507C2314yes—
121C2×#1143—24no—
122C2×#1143—42no—
123C2×#1143C2314yes—
124C2×#1143C2314yes—
125#6493—22no—
126#6493C2314yes—
127C4×C22⋊D7—28no—
128C4×C22⋊D7D414yes—
129C4×C22⋊D7C2314yes—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4D411yescharacteristic
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139#6487—22no—
140#6487—28no—
141#6487C2314yes—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4D411yescharacteristic
148C2×C4×Dic7—21no—
149C2×C4×Dic7—21no—
150C2×C4×Dic7C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C2×#1132—42no—
154C2×#1132C2314yes—
155C2×#1131—42no—
156C2×#1131C2314yes—
157#6458—22no—
158#6458C2314yes—
159#6456—22no—
160#6456C2314yes—
161#6455—22no—
162#6455C2314yes—
163#6451—22no—
164#6451C2314yes—
165#6448—28no—
166#6447—28no—
167#6438—28no—
168#6435—28no—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175C22⋊(C7⋊C8)C2314yes—
176#6395C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6392C2314yes—
179#6390C2314yes—
180Dic7⋊C8C2314yes—
181C8×Dic7C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6382C2314yes—
185#6381C2314yes—
186C2×#555—71no—
187C2×D4×Q8—71no—
188#3329—716no—
189C2×#487—71no—
190C2×#485—71no—
191C2×#485—71no—
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×#419D711yescharacteristic, complemented
202C24×C7C2×D411yescharacteristic
203C23×D7—21no—
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—24no—
207C2×C7×Q8—21no—
208C2×C7×Q8—22no—
209C2×C7×Q8—28no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—44no—
213C2×C7×Q8—44no—
214C2×C7×Q8—48no—
215C2×C7×Q8#4114yes—
216C2×C7×Q8C2412yes—
217C2×C7×Q8C2412yes—
218C22×C4×C7—21no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—24no—
225C22×C4×C7—44no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2411yescharacteristic
230C2×C22⋊D7—24no—
231C2×C22⋊D7—24no—
232C2×C22⋊D7—82no—
233C2×C22⋊D7C2×D414yes—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7C2×D411yescharacteristic
238C22×Dic7C2×D411yescharacteristic
239C22×Dic7C2×D411yescharacteristic
240Q8×D7—28no—
241Q8×D7—44no—
242Q8×D7—48no—
243C2×D28—22no—
244C2×D28—22no—
245C2×D28—21no—
246C2×D28—24no—
247C2×D28—82no—
248C2×D28C2412yes—
249C2×C4×D7—22no—
250C2×C4×D7—22no—
251C2×C4×D7—24no—
252C2×C4×D7—24no—
253C2×C4×D7—44no—
254C2×C4×D7—44no—
255C2×C4×D7C2×D412yes—
256C2×C4×D7C2412yes—
257C2×Dic14—22no—
258C2×Dic14—22no—
259C2×Dic14—21no—
260C2×Dic14—24no—
261C2×Dic14—24no—
262C2×Dic14—44no—
263C2×Dic14—82no—
264C2×Dic14C2412yes—
265C7×M16—44no—
266C2×C7×C8—22no—
267C2×C7×C8—22no—
268C2×C7×C8C2412yes—
269C2×C7×C8C2412yes—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4C2412yes—
273C7×C4⋊C4C2412yes—
274C7×C22⋊C4—24no—
275C42×C7—24no—
276C22⋊Dic7—24no—
277C22⋊Dic7C2×D414yes—
278#1143—28no—
279#1143—44no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4C2×D414yes—
286C4⋊Dic7—21no—
287C4⋊Dic7—21no—
288C4⋊Dic7—24no—
289C4⋊Dic7C2412yes—
290C4⋊Dic7C2412yes—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4C2×D414yes—
297C4×Dic7—24no—
298C4×Dic7—24no—
299C4×Dic7C2×D412yes—
300C4×Dic7C2412yes—
301C2×C7⋊C8—22no—
302C2×C7⋊C8—22no—
303C2×C7⋊C8C2412yes—
304C2×C7⋊C8C2412yes—
305#1132—44no—
306#1131—44no—
307C23×Q8—71no—
308C23×Q8C2×D711yescharacteristic
309C22×SD16—71no—
310C22×SD16—71no—
311C22×SD16—71no—
312C22×M16—71no—
313C22×M16C2×D711yescharacteristic
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—71no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8—141no—
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#485—78no—
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×#107—71no—
350C2×#106—71no—
351C2×C4⋊C8—71no—
352#419—78no—
353#419C2×D718yescomplemented
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103C2×D711yescharacteristic
360C2×#103C2×D711yescharacteristic
361C2×#103C2×D711yescharacteristic
362C2×#103C2×D711yescharacteristic
363C2×#102—71no—
364C2×C22⋊C8—71no—
365C2×C22⋊C8—71no—
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—24no—
381C7×Q8—22no—
382C7×Q8—22no—
383C7×Q8—22no—
384C7×Q8—48no—
385C7×Q8—42no—
386C7×Q8C2×#4114yes—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—24no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—48no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—42no—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D411yescharacteristic
402C2×C4×C7C2×#4112yes—
403C2×C4×C7H(5,𝔽2)12yes—
404C2×C4×C7C2511yescharacteristic
405C22⋊D7—28no—
406C22⋊D7—84no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414C2×Dic7—42no—
415C2×Dic7#13714yes—
416C2×Dic7C22×D412yes—
417C2×Dic7C22×D412yes—
418C2×Dic7C22×D412yes—
419D28—22no—
420D28—22no—
421D28—42no—
422D28—84no—
423C4×D7—24no—
424C4×D7—22no—
425C4×D7—22no—
426C4×D7—48no—
427C4×D7—48no—
428Dic14—22no—
429Dic14—22no—
430Dic14—48no—
431Dic14—42no—
432Dic14—84no—
433C7×C8—22no—
434C7×C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—24no—
440C22×Q8—42no—
441C22×Q8—74no—
442C22×Q8—71no—
443C22×Q8—141no—
444C22×Q8—141no—
445C22×Q8—142no—
446C22×Q8—144no—
447C22×Q8—282no—
448C22×Q8C22×D711yescharacteristic
449C22×Q8C22×D714yes—
450C22×Q8C22×D711yescharacteristic
451C22×D4—71no—
452C22×D4—71no—
453C22×D4—141no—
454C22×D4—141no—
455C23×C4—21no—
456C23×C4—71no—
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—42no—
467C2×M16—74no—
468C2×M16—282no—
469C2×M16C22×D714yes—
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—74no—
482C22⋊Q8—74no—
483C22⋊Q8—148no—
484C22⋊Q8—148no—
485C22⋊Q8—142no—
486C22⋊Q8—142no—
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—71no—
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⋊C4—141no—
513C2×C4⋊C4C22×D711yescharacteristic
514C2×C4⋊C4C22×D711yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—71no—
517C2×C22⋊C4—71no—
518C2×C22⋊C4—141no—
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#107—74no—
530#106—74no—
531C4⋊C8—74no—
532#103—74no—
533#103—74no—
534#103—74no—
535#103—74no—
536#103—74no—
537#103C22×D714yes—
538#103C22×D714yes—
539#103C22×D714yes—
540#103C22×D714yes—
541#102—74no—
542C22⋊C8—74no—
543C22⋊C8—74no—
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—24no—
562C4×C7—22no—
563C4×C7—42no—
564C4×C7—42no—
565C4×C7—42no—
566C4×C7#54612yes—
567C4×C7C22×#4111yescharacteristic
568C4×C7C2×H(5,𝔽2)11yescharacteristic
569Dic7—22no—
570Dic7—22no—
571Dic7—42no—
572Dic7—42no—
573Dic7—42no—
574Dic7C2×#13714yes—
575C24—71no—
576C24—141no—
577C24D4×D711yescharacteristic
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—28no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—48no—
588C2×Q8—72no—
589C2×Q8—144no—
590C2×Q8—144no—
591C2×Q8—141no—
592C2×Q8—148no—
593C2×Q8—142no—
594C2×Q8—142no—
595C2×Q8—284no—
596C2×Q8—284no—
597C2×Q8—288no—
598C2×Q8—562no—
599C2×Q8#115714yes—
600C2×Q8C23×D712yes—
601C2×Q8C23×D712yes—
602C2×D4—74no—
603C2×D4—72no—
604C2×D4—144no—
605C2×D4—144no—
606C2×D4—144no—
607C2×D4—142no—
608C2×D4—141no—
609C2×D4—142no—
610C2×D4—562no—
611C2×D4—562no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—44no—
620C22×C4—71no—
621C22×C4—71no—
622C22×C4—71no—
623C22×C4—72no—
624C22×C4—72no—
625C22×C4—144no—
626C22×C4—144no—
627C22×C4—142no—
628C22×C4—142no—
629C22×C4—141no—
630C22×C4—141no—
631C22×C4—141no—
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—44no—
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—21no—
652C4⋊C4—21no—
653C4⋊C4—74no—
654C4⋊C4—72no—
655C4⋊C4—72no—
656C4⋊C4—144no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4—144no—
662C4⋊C4—141no—
663C4⋊C4—141no—
664C4⋊C4C23×D712yes—
665C4⋊C4C23×D712yes—
666C22⋊C4—24no—
667C22⋊C4—74no—
668C22⋊C4—74no—
669C22⋊C4—144no—
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—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—42no—
706Q8—142no—
707Q8—142no—
708Q8—288no—
709Q8—282no—
710Q8—564no—
711Q8C2×#115714yes—
712D4—148no—
713D4—142no—
714D4—142no—
715D4—282no—
716D4—564no—
717D4—564no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—74no—
732C2×C4—72no—
733C2×C4—72no—
734C2×C4—72no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—144no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—288no—
744C2×C4—288no—
745C2×C4—282no—
746C2×C4—282no—
747C2×C4—282no—
748C2×C4C2×#115712yes—
749C2×C4C2×D4×D712yes—
750C2×C4C2×D4×D711yescharacteristic
751C2×C4#654812yes—
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#9018112yes—
771C22D7×#13712yes—
772C22#9046912yes—
773C22C22×D4×D711yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—74no—
780C4—142no—
781C4—142no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9018112yes—
786C4C22×#115711yescharacteristic
787C4C2×#654811yescharacteristic
788C2—42no—
789C2—282no—
790C2—562no—
791C2#1173641814yesdirect product factor
792C2C2×#9018111yescharacteristic
793C2C2×D7×#13711yescharacteristic
794C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#419C2
socleC23×C7C22×D4
prime radicalC2×#90223C2
hypercenterC2×#419D7
hypocenterC7C2×#3329
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D7C2semidirect
3. C2×C7×#419C2semidirect
4. C2×#89999C2semidirect
5. C2×#89906C2semidirect
6. C2×#89900C2semidirect
7. C2×#89768C2semidirect
8. #11736418C2direct (N × H)
9. C2×#89590C2semidirect
10. C2×#89584C2semidirect
11. C2×#89578C2semidirect
12. C2×#89574C2semidirect
13. C2×#89564C2semidirect
14. C2×#89586C2semidirect
15. C2×#89566C2semidirect
16. C2×#89560C2semidirect
22. Q8×C22⋊D7C22semidirect
47. C7×#419C22semidirect
52. #89999C22semidirect
56. #89906C22semidirect
57. #89900C22semidirect
64. #89768C22semidirect
69. #89590C22semidirect
70. #89586C22semidirect
71. #89584C22semidirect
72. #89578C22semidirect
73. #89574C22semidirect
74. #89566C22semidirect
75. #89564C22semidirect
76. #89560C22semidirect
201. C2×#419D7semidirect
353. #419C2×D7semidirect
681. C2×C7#3329semidirect
757. C7C2×#3329semidirect
791. C2#11736418direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D72
C2×#902232
C2×C7×#4192
C2×#899992
C2×#899062
C2×#899002
C2×#897682
#117364182
C2×#895902
C2×#895842
C2×#895782
C2×#895742
C2×#895642
C2×#895862
C2×#895662
C2×#895602
C2×#33297