Finite Group Databasebeta

← C2×#11738370 #14230712

Subgroups — C2×#11738370 #14230712

Order 1792.

2158 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×#90322C211yesmaximal, characteristic
2C2×#90326C211yesmaximal, characteristic, complemented
3C2×C7×#470C211yesmaximal, characteristic, complemented
4C2×#89959C211yesmaximal, characteristic, complemented
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89905C211yesmaximal, characteristic, complemented
7C2×#89900C211yesmaximal, characteristic, complemented
8C2×#89819C211yesmaximal, characteristic, complemented
9C2×#89815C211yesmaximal, characteristic, complemented
10#11738370C2116yesmaximal, direct product factor
11C2×#89642C211yesmaximal, characteristic, complemented
12C2×#89634C211yesmaximal, characteristic, complemented
13C2×#89588C211yesmaximal, characteristic, complemented
14C2×#89575C211yesmaximal, characteristic, complemented
15C2×#89564C211yesmaximal, characteristic, complemented
16C2×#89560C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×#6509C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×#6507C2211yescharacteristic
26C22×#1144C2211yescharacteristic
27C22×#1143C2211yescharacteristic
28C2×C4×C22⋊D7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×#1131C2211yescharacteristic
31#90326—24no—
32#90326C2218yescomplemented
33#90322—24no—
34#90322C2218yes—
35C2×#6460—21no—
36C2×#6460C2211yescharacteristic
37C2×#6457—21no—
38C2×#6456C2211yescharacteristic
39C2×D7×C4⋊C4—21no—
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6452—21no—
42C2×#6451C2211yescharacteristic
43C2×#6447—21no—
44C2×#6446—21no—
45C2×(C22⋊D7)⋊C4—21no—
46C2×#6441—21no—
47C7×#470C2218yescomplemented
48C2×C7×#106C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89959C2218yescomplemented
55#89954C2218yescomplemented
56#89905C2218yescomplemented
57#89900C2218yescomplemented
58C2×#6395C2211yescharacteristic
59C2×#6395C2211yescharacteristic
60C2×(C2×D7)⋊C8C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×C8×Dic7C2211yescharacteristic
65#89819C2218yescomplemented
66#89815C2218yescomplemented
67C2×#6384C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71#89642C2218yescomplemented
72#89634C2218yescomplemented
73#89588C2218yescomplemented
74#89575C2218yescomplemented
75#89564C2218yescomplemented
76#89560C2218yescomplemented
77C2×#3331—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C23×Dic7—21no—
84C2×#1161—22no—
85C2×#1161—24no—
86C2×#1161—42no—
87C2×#1161C2314yes—
88C2×#1157—22no—
89C2×#1157—24no—
90C2×#1157—42no—
91C2×#1157C2314yes—
92C22×D28—21no—
93C22×D28C2311yescharacteristic
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×C4×D7—21no—
97C22×C4×D7—21no—
98C22×C4×D7C2311yescharacteristic
99C22×Dic14—21no—
100C22×Dic14C2311yescharacteristic
101C2×C7×Q16—42no—
102C2×C7×Q16C2314yes—
103C2×C7×M16—42no—
104C2×C7×M16C2314yes—
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2311yescharacteristic
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8C2314yes—
110C7×C22⋊Q8C2314yes—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C22⋊Dic7D411yescharacteristic
118#6509—22no—
119#6509C2314yes—
120Q8×Dic7—22no—
121Q8×Dic7C2314yes—
122#6507—22no—
123#6507C2314yes—
124C2×#1144—42no—
125C2×#1144C2314yes—
126C2×#1143—24no—
127C2×#1143C2314yes—
128C4×C22⋊D7D414yes—
129C4×C22⋊D7C2314yes—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4D411yescharacteristic
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7—22no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×C4⋊Dic7C2314yes—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4D411yescharacteristic
147C2×C4×Dic7—21no—
148C2×C4×Dic7C2311yescharacteristic
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C2×#1131—42no—
152C2×#1131C2314yes—
153#6460—22no—
154#6460—28no—
155#6460C2314yes—
156#6457—28no—
157#6456—22no—
158#6456C2314yes—
159D7×C4⋊C4—22no—
160D7×C4⋊C4—28no—
161D7×C4⋊C4C2314yes—
162#6452—28no—
163#6451—22no—
164#6451C2314yes—
165#6447—28no—
166#6446—28no—
167(C22⋊D7)⋊C4—28no—
168#6441—28no—
169C7×#106C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174C22⋊(C7⋊C8)C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180Dic7⋊C8C2314yes—
181C8×Dic7C2314yes—
182#6384C2314yes—
183#6383C2314yes—
184#6382C2314yes—
185#6382C2314yes—
186C2×#554—71no—
187C2×#547—71no—
188#3331—716no—
189C2×#487—71no—
190C2×#483—71no—
191C2×#483—71no—
192C2×#476—71no—
193C2×#470—71no—
194C2×#470D711yescharacteristic, complemented
195C2×#462—71no—
196C2×#452—71no—
197C2×#452—71no—
198C2×C4×SD16—71no—
199C2×#436—71no—
200C2×#417—71no—
201C2×#417—71no—
202C24×C7C2×D411yescharacteristic
203C23×D7—21no—
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8C2412yes—
212C2×C7×Q8C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2411yescharacteristic
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—44no—
226C2×C22⋊D7C2×D414yes—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—24no—
231C22×Dic7—82no—
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235#1161—28no—
236#1161—44no—
237#1161—48no—
238#1157—28no—
239#1157—44no—
240#1157—48no—
241C2×D28—21no—
242C2×D28—22no—
243C2×D28—24no—
244C2×D28—44no—
245C2×D28#4114yes—
246C2×D28C2412yes—
247C2×C4×D7—22no—
248C2×C4×D7—22no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—24no—
252C2×C4×D7—24no—
253C2×C4×D7—44no—
254C2×C4×D7—44no—
255C2×C4×D7—44no—
256C2×C4×D7—82no—
257C2×C4×D7C2×D412yes—
258C2×C4×D7C2412yes—
259C2×Dic14—22no—
260C2×Dic14—22no—
261C2×Dic14—21no—
262C2×Dic14—24no—
263C2×Dic14—82no—
264C2×Dic14C2412yes—
265C7×Q16—44no—
266C7×M16—44no—
267C2×C7×C8—22no—
268C2×C7×C8—22no—
269C2×C7×C8C2412yes—
270C2×C7×C8C2412yes—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—24no—
273C7×C4⋊C4—24no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4C2412yes—
276C7×C4⋊C4C2412yes—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—24no—
279C22⋊Dic7C2×D414yes—
280#1144—44no—
281#1143—28no—
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—24no—
288C4⋊Dic7—21no—
289C4⋊Dic7—24no—
290C4⋊Dic7—24no—
291C4⋊Dic7C2412yes—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298Dic7⋊C4C2×D414yes—
299C4×Dic7—24no—
300C4×Dic7C2×D412yes—
301C4×Dic7C2412yes—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306#1131—44no—
307C22×#41—71no—
308C22×#41—71no—
309C22×Q16—71no—
310C22×Q16C2×D711yescharacteristic
311C22×SD16—71no—
312C22×M16—71no—
313C22×M16C2×D711yescharacteristic
314#554—78no—
315#554—144no—
316#547—78no—
317#547—144no—
318C2×C4⋊Q8—71no—
319C2×C4⋊Q8—71no—
320C2×#125—141no—
321C2×#123—141no—
322C2×#123—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—71no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8—141no—
327C2×C22⋊Q8C2×D711yescharacteristic
328C2×C22⋊Q8C2×D711yescharacteristic
329C2×#121—141no—
330C2×C4×Q8—71no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C22×C4⋊C4—71no—
335C22×C4⋊C4—71no—
336C22×C4⋊C4—141no—
337#487—78no—
338#483—78no—
339#483—78no—
340#476—78no—
341#470—78no—
342#470C2×D718yescomplemented
343#462—78no—
344#452—78no—
345#452—78no—
346C4×SD16—78no—
347#436—78no—
348C2×#106—71no—
349C2×#106—71no—
350C2×#106C2×D711yescharacteristic
351C2×C4⋊C8—71no—
352#417—78no—
353#417—78no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103C2×D711yescharacteristic
360C2×#103C2×D711yescharacteristic
361C2×#102—71no—
362C2×#102—71no—
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—24no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7C22×D412yes—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—22no—
383C7×Q8—22no—
384C7×Q8—42no—
385C7×Q8—42no—
386C2×C4×C7—22no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D411yescharacteristic
400C2×C4×C7C2×#4112yes—
401C2×C4×C7H(5,𝔽2)12yes—
402C2×C4×C7C2511yescharacteristic
403C22⋊D7—28no—
404C22⋊D7—48no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—42no—
411C2×Dic7—42no—
412C2×Dic7—42no—
413C2×Dic7—84no—
414C2×Dic7#13714yes—
415C2×Dic7C22×D412yes—
416C2×Dic7C22×D412yes—
417C2×Dic7C22×D412yes—
418D28—24no—
419D28—22no—
420D28—48no—
421D28C2×#4114yes—
422C4×D7—24no—
423C4×D7—22no—
424C4×D7—22no—
425C4×D7—48no—
426C4×D7—48no—
427C4×D7—48no—
428C4×D7—84no—
429Dic14—22no—
430Dic14—22no—
431Dic14—42no—
432Dic14—84no—
433C7×C8—22no—
434C7×C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C2×#41—74no—
438C2×#41—74no—
439C2×#41—144no—
440C2×#41—142no—
441C2×#41—142no—
442C2×#41—144no—
443C2×#41—282no—
444C2×#41—282no—
445C22×Q8—71no—
446C22×Q8—141no—
447C22×Q8C22×D711yescharacteristic
448C22×Q8C22×D711yescharacteristic
449C22×D4—71no—
450C22×D4—71no—
451C22×D4—141no—
452C22×D4—141no—
453C23×C4—71no—
454C23×C4—141no—
455C23×C4—141no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4—141no—
459C23×C4C22×D711yescharacteristic
460C2×Q16—42no—
461C2×Q16—74no—
462C2×Q16—282no—
463C2×Q16C22×D714yes—
464C2×SD16—74no—
465C2×SD16—144no—
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—
478#125—148no—
479#123—148no—
480#123—148no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—74no—
484C22⋊Q8—74no—
485C22⋊Q8—148no—
486C22⋊Q8—148no—
487C22⋊Q8—142no—
488C22⋊Q8—142no—
489C22⋊Q8C22×D714yes—
490C22⋊Q8C22×D714yes—
491#121—148no—
492C4×Q8—74no—
493C4×Q8—142no—
494C4×D4—74no—
495C4×D4—74no—
496C4×D4—74no—
497C4×D4—142no—
498C4×D4—148no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—71no—
502C2×C4⋊C4—71no—
503C2×C4⋊C4—71no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—148no—
507C2×C4⋊C4—142no—
508C2×C4⋊C4—141no—
509C2×C4⋊C4—141no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4C22×D711yescharacteristic
518C2×C4⋊C4C22×D711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—71no—
522C2×C22⋊C4—71no—
523C2×C22⋊C4—141no—
524C2×C22⋊C4—141no—
525C2×C22⋊C4—141no—
526C2×C42—71no—
527C2×C42—141no—
528#106—74no—
529#106—74no—
530#106C22×D714yes—
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#102—74no—
540#102—74no—
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—24no—
555C2×D7—22no—
556C2×D7—22no—
557C2×D7—44no—
558C2×D7—48no—
559C2×D7—42no—
560C2×D7—42no—
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—22no—
570Dic7—22no—
571Dic7—42no—
572Dic7—42no—
573Dic7—42no—
574Dic7C2×#13714yes—
575C24—71no—
576C24—141no—
577C24D4×D711yescharacteristic
578#41—148no—
579#41—148no—
580#41—284no—
581#41—288no—
582#41—284no—
583#41—288no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—72no—
591C2×Q8—144no—
592C2×Q8—141no—
593C2×Q8—142no—
594C2×Q8—142no—
595C2×Q8—562no—
596C2×Q8C23×D712yes—
597C2×Q8C23×D712yes—
598C2×D4—74no—
599C2×D4—74no—
600C2×D4—72no—
601C2×D4—144no—
602C2×D4—144no—
603C2×D4—144no—
604C2×D4—141no—
605C2×D4—142no—
606C2×D4—284no—
607C2×D4—284no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—71no—
615C22×C4—71no—
616C22×C4—71no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—144no—
620C22×C4—144no—
621C22×C4—144no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—141no—
625C22×C4—141no—
626C22×C4—141no—
627C22×C4—144no—
628C22×C4—144no—
629C22×C4—284no—
630C22×C4—284no—
631C22×C4—284no—
632C22×C4—562no—
633C22×C4—562no—
634C22×C4D4×D712yes—
635C22×C4D4×D711yescharacteristic
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638Q16—44no—
639Q16—284no—
640SD16—148no—
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—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—74no—
656C4⋊C4—72no—
657C4⋊C4—72no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4—144no—
662C4⋊C4—144no—
663C4⋊C4—144no—
664C4⋊C4—144no—
665C4⋊C4—141no—
666C4⋊C4—144no—
667C4⋊C4—141no—
668C4⋊C4C23×D712yes—
669C4⋊C4C23×D712yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—74no—
673C22⋊C4—74no—
674C22⋊C4—144no—
675C22⋊C4—144no—
676C22⋊C4—144no—
677C42—72no—
678C42—72no—
679C42—144no—
680C2×C7—42no—
681C2×C7#333114yescomplemented
682C2×C7C2×#54611yescharacteristic
683C2×C7C22×#13711yescharacteristic
684C2×C7C2×#57711yescharacteristic
685D7—42no—
686D7—44no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—72no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23—144no—
695C23—142no—
696C23—282no—
697C23—282no—
698C23C2×D4×D712yes—
699C23C2×D4×D711yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—42no—
706Q8—142no—
707Q8—142no—
708Q8—282no—
709Q8—564no—
710D4—74no—
711D4—148no—
712D4—144no—
713D4—142no—
714D4—288no—
715D4—288no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—74no—
729C2×C4—72no—
730C2×C4—72no—
731C2×C4—72no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—144no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—288no—
741C2×C4—288no—
742C2×C4—288no—
743C2×C4—282no—
744C2×C4—282no—
745C2×C4—282no—
746C2×C4—564no—
747C2×C4—564no—
748C2×C4C2×D4×D712yes—
749C2×C4C2×D4×D711yescharacteristic
750C2×C4#654812yes—
751C2×C4D7×#4112yes—
752C2×C4C24×D711yescharacteristic
753C8—22no—
754C8—22no—
755C8—142no—
756C8—142no—
757C7C2×#333111yescharacteristic, complemented, Sylow
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—142no—
763C22—142no—
764C22—142no—
765C22—144no—
766C22—284no—
767C22—288no—
768C22—282no—
769C22—282no—
770C22#9030112yes—
771C22D7×#13712yes—
772C22#9046912yes—
773C22C22×D4×D711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—74no—
780C4—142no—
781C4—142no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9030112yes—
786C4C2×#654811yescharacteristic
787C4C2×D7×#4111yescharacteristic
788C2—42no—
789C2—282no—
790C2—284no—
791C2#1173837014yesdirect product factor
792C2C2×#9030111yescharacteristic
793C2C2×D7×#13711yescharacteristic
794C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#470C2
socleC23×C7C22×D4
prime radicalC2×#90322C2
hypercenterC2×#470D7
hypocenterC7C2×#3331
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×#90326C2semidirect
3. C2×C7×#470C2semidirect
4. C2×#89959C2semidirect
5. C2×#89954C2semidirect
6. C2×#89905C2semidirect
7. C2×#89900C2semidirect
8. C2×#89819C2semidirect
9. C2×#89815C2semidirect
10. #11738370C2direct (N × H)
11. C2×#89642C2semidirect
12. C2×#89634C2semidirect
13. C2×#89588C2semidirect
14. C2×#89575C2semidirect
15. C2×#89564C2semidirect
16. C2×#89560C2semidirect
32. #90326C22semidirect
47. C7×#470C22semidirect
54. #89959C22semidirect
55. #89954C22semidirect
56. #89905C22semidirect
57. #89900C22semidirect
65. #89819C22semidirect
66. #89815C22semidirect
71. #89642C22semidirect
72. #89634C22semidirect
73. #89588C22semidirect
74. #89575C22semidirect
75. #89564C22semidirect
76. #89560C22semidirect
194. C2×#470D7semidirect
342. #470C2×D7semidirect
681. C2×C7#3331semidirect
757. C7C2×#3331semidirect
791. C2#11738370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903222
C2×#903262
C2×C7×#4702
C2×#899592
C2×#899542
C2×#899052
C2×#899002
C2×#898192
C2×#898152
#117383702
C2×#896422
C2×#896342
C2×#895882
C2×#895752
C2×#895642
C2×#895602
C2×#33317