Finite Group Databasebeta

← C2×#11738139 #14230424

Subgroups — C2×#11738139 #14230424

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×#90323C211yesmaximal, characteristic, complemented
2C2×#90309C211yesmaximal, characteristic
3C2×C7×#465C211yesmaximal, characteristic, complemented
4C2×#89942C211yesmaximal, characteristic, complemented
5C2×#89934C211yesmaximal, characteristic, complemented
6C22×#6390C211yesmaximal, characteristic, complemented
7C2×#89883C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89812C211yesmaximal, characteristic, complemented
10#11738139C2116yesmaximal, direct product factor
11C2×#89629C211yesmaximal, characteristic, complemented
12C2×#89639C211yesmaximal, characteristic, complemented
13C2×#89574C211yesmaximal, characteristic, complemented
14C2×#89569C211yesmaximal, characteristic, complemented
15C2×#89552C211yesmaximal, characteristic, complemented
16C2×#89529C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C23×Dic14C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C2×C7×C22⋊Q8C2211yescharacteristic
22C2×C7×#121C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C2×#6502—21no—
25C2×#6501C2211yescharacteristic
26C2×D4×Dic7—21no—
27C2×D4×Dic7C2211yescharacteristic
28C22×#1142C2211yescharacteristic
29C22×#1142C2211yescharacteristic
30C2×C4×C22⋊D7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×#1131C2211yescharacteristic
33#90323—24no—
34#90323C2218yescomplemented
35#90309—24no—
36#90309C2218yes—
37C2×#6460C2211yescharacteristic
38C2×#6459—21no—
39C2×#6455C2211yescharacteristic
40C2×#6453C2211yescharacteristic
41C2×#6451—21no—
42C2×#6450C2211yescharacteristic
43C2×#6449—21no—
44C2×(C22⋊D7)⋊C4—21no—
45C2×#6442—21no—
46C2×#6441—21no—
47C7×#465C2218yescomplemented
48C2×C7×#106C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×C22⋊(C7⋊C8)C2211yescharacteristic
54#89942C2218yescomplemented
55#89934C2218yescomplemented
56#89883C2218yescomplemented
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6390C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6390C2211yescharacteristic
61C2×#6390C2211yescharacteristic
62C2×#6390C2218yescomplemented
63C2×#6389C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65#89816C2218yescomplemented
66#89812C2218yescomplemented
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89639C2218yescomplemented
72#89629C2218yescomplemented
73#89574C2218yescomplemented
74#89569C2218yescomplemented
75#89552C2218yescomplemented
76#89529C2218yescomplemented
77C2×#3320—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7D411yescharacteristic
84C23×Dic7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C2×Q8×D7—22no—
88C2×Q8×D7—24no—
89C2×Q8×D7—42no—
90C2×Q8×D7C2314yes—
91C22×C4×D7—21no—
92C22×C4×D7C2311yescharacteristic
93C22×Dic14—24no—
94C22×Dic14—21no—
95C22×Dic14—22no—
96C22×Dic14—21no—
97C22×Dic14—42no—
98C22×Dic14C2311yescharacteristic
99C22×Dic14C2314yes—
100C22×Dic14C2311yescharacteristic
101C2×C7×SD16—42no—
102C2×C7×SD16C2314yes—
103C22×C7×C8—42no—
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2314yes—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8C2314yes—
109C7×#121—22no—
110C7×#121C2314yes—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118C2×C22⋊Dic7D411yescharacteristic
119#6507—22no—
120#6507C2314yes—
121#6502—28no—
122#6501—22no—
123#6501C2314yes—
124D4×Dic7—28no—
125D4×Dic7—22no—
126D4×Dic7C2314yes—
127C2×#1142—24no—
128C2×#1142—42no—
129C2×#1142C2314yes—
130C2×#1142C2314yes—
131C4×C22⋊D7D414yes—
132C4×C22⋊D7C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4D411yescharacteristic
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—22no—
138C2×C4⋊Dic7—21no—
139C2×C4⋊Dic7—21no—
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yes—
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×#1131—42no—
154C2×#1131C2314yes—
155#6460—22no—
156#6460C2314yes—
157#6459—28no—
158#6455—22no—
159#6455C2314yes—
160#6453—22no—
161#6453C2314yes—
162#6451—28no—
163#6450—22no—
164#6450C2314yes—
165#6449—28no—
166(C22⋊D7)⋊C4—28no—
167#6442—28no—
168#6441—28no—
169C7×#106C2314yes—
170C7×#103C2314yes—
171C7×#102C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174C22⋊(C7⋊C8)C2314yes—
175(C2×D7)⋊C8C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178#6390C2314yes—
179#6390C2314yes—
180#6389C2314yes—
181Dic7⋊C8C2314yes—
182#6384C2314yes—
183#6384C2314yes—
184#6381C2314yes—
185#6381C2314yes—
186C2×#553—71no—
187C2×D4×Q8—71no—
188#3320—716no—
189C2×#491—71no—
190C2×#484—71no—
191C2×#485—71no—
192C2×#479—71no—
193C2×#468—71no—
194C2×#465D711yescharacteristic, complemented
195C2×#461—71no—
196C2×#448—71no—
197C2×#448—71no—
198C2×#440—71no—
199C2×#435—71no—
200C2×#419—71no—
201C22×#103—71no—
202C24×C7—21no—
203C24×C7C2×D411yescharacteristic
204C23×D7C2×D411yescharacteristic
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8C2412yes—
209C2×C7×D4—24no—
210C2×C7×D4—21no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—44no—
214C2×C7×D4C2412yes—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2412yes—
223C22×C4×C7C2411yescharacteristic
224C2×C22⋊D7—24no—
225C2×C22⋊D7—24no—
226C2×C22⋊D7—82no—
227C2×C22⋊D7C2×D414yes—
228C22×Dic7—21no—
229C22×Dic7—24no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—24no—
234C22×Dic7—24no—
235C22×Dic7—44no—
236C22×Dic7—82no—
237C22×Dic7—82no—
238C22×Dic7C2×D411yescharacteristic
239C22×Dic7C2×D411yescharacteristic
240C22×Dic7C2×D411yescharacteristic
241Q8×D7—28no—
242Q8×D7—44no—
243Q8×D7—48no—
244C2×C4×D7—22no—
245C2×C4×D7—22no—
246C2×C4×D7—24no—
247C2×C4×D7—44no—
248C2×C4×D7C2×D412yes—
249C2×C4×D7C2412yes—
250C2×Dic14—21no—
251C2×Dic14—22no—
252C2×Dic14—22no—
253C2×Dic14—22no—
254C2×Dic14—28no—
255C2×Dic14—24no—
256C2×Dic14—21no—
257C2×Dic14—24no—
258C2×Dic14—44no—
259C2×Dic14—48no—
260C2×Dic14—44no—
261C2×Dic14—44no—
262C2×Dic14#4114yes—
263C2×Dic14C2412yes—
264C2×Dic14C2412yes—
265C7×SD16—44no—
266C2×C7×C8—22no—
267C2×C7×C8—22no—
268C2×C7×C8—44no—
269C2×C7×C8C2412yes—
270C2×C7×C8C2412yes—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—24no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C22⋊C4—24no—
277C7×C22⋊C4—24no—
278C22⋊Dic7—24no—
279C22⋊Dic7—24no—
280C22⋊Dic7C2×D414yes—
281#1142—28no—
282#1142—44no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4C2×D414yes—
286C4⋊Dic7—24no—
287C4⋊Dic7—21no—
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⋊C4C2×D414yes—
298C4×Dic7—24no—
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—
307C23×Q8—71no—
308C23×Q8—71no—
309C22×SD16—71no—
310C22×SD16—71no—
311C22×SD16C2×D711yescharacteristic
312C22×M16—71no—
313C23×C8C2×D711yescharacteristic
314#553—78no—
315#553—144no—
316D4×Q8—78no—
317D4×Q8—144no—
318C2×C4⋊Q8—71no—
319C2×C4⋊Q8—141no—
320C2×#126—141no—
321C2×#125—71no—
322C2×#123—141no—
323C2×C22⋊Q8—71no—
324C2×C22⋊Q8—141no—
325C2×C22⋊Q8—141no—
326C2×C22⋊Q8C2×D711yescharacteristic
327C2×#121—71no—
328C2×#121—141no—
329C2×#121C2×D711yescharacteristic
330C2×C4×Q8—71no—
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—141no—
334C2×C4×D4—141no—
335C2×#117—71no—
336C22×C4⋊C4—71no—
337#491—78no—
338#485—78no—
339#484—78no—
340#479—78no—
341#468—78no—
342#465C2×D718yescomplemented
343#461—78no—
344#448—78no—
345#448—78no—
346#440—78no—
347#435—78no—
348C2×#107—71no—
349C2×#107—71no—
350C2×#106C2×D711yescharacteristic
351C2×C4⋊C8—71no—
352#419—78no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—78no—
360C2×#103—71no—
361C2×#103—71no—
362C2×#103C2×D711yescharacteristic
363C2×#102C2×D711yescharacteristic
364C2×C22⋊C8—71no—
365C2×C22⋊C8—71no—
366C2×#97—71no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7—42no—
373C23×C7#13714yes—
374C23×C7C22×D412yes—
375C23×C7C22×D411yescharacteristic
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7C22×D412yes—
380C7×Q8—22no—
381C7×Q8—22no—
382C7×Q8—42no—
383C7×D4—22no—
384C7×D4—22no—
385C7×D4—48no—
386C7×D4—42no—
387C2×C4×C7—22no—
388C2×C4×C7—24no—
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×C7C22×D412yes—
398C2×C4×C7C22×D411yescharacteristic
399C2×C4×C7C2×#4112yes—
400C2×C4×C7H(5,𝔽2)12yes—
401C2×C4×C7C2511yescharacteristic
402C22⋊D7—28no—
403C22⋊D7—84no—
404C2×Dic7—24no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—22no—
412C2×Dic7—48no—
413C2×Dic7—42no—
414C2×Dic7—42no—
415C2×Dic7—42no—
416C2×Dic7—84no—
417C2×Dic7—84no—
418C2×Dic7C22×D412yes—
419C2×Dic7C22×D412yes—
420C2×Dic7C22×D412yes—
421C4×D7—24no—
422C4×D7—22no—
423C4×D7—22no—
424C4×D7—48no—
425Dic14—24no—
426Dic14—22no—
427Dic14—22no—
428Dic14—22no—
429Dic14—48no—
430Dic14—48no—
431Dic14—42no—
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—144no—
443C22×Q8—142no—
444C22×Q8—141no—
445C22×Q8—142no—
446C22×Q8—144no—
447C22×Q8—282no—
448C22×Q8—282no—
449C22×Q8C22×D711yescharacteristic
450C22×D4—21no—
451C22×D4—71no—
452C22×D4—141no—
453C22×D4C22×D711yescharacteristic
454C23×C4—71no—
455C23×C4—141no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4—141no—
459C23×C4C22×D711yescharacteristic
460C2×SD16—42no—
461C2×SD16—74no—
462C2×SD16—74no—
463C2×SD16—144no—
464C2×SD16—282no—
465C2×SD16C22×D714yes—
466C2×M16—74no—
467C2×M16—282no—
468C22×C8—42no—
469C22×C8—71no—
470C22×C8—71no—
471C22×C8C22×D711yescharacteristic
472C22×C8C22×D711yescharacteristic
473C22×C8C22×D714yes—
474C4⋊Q8—74no—
475C4⋊Q8—142no—
476C4⋊Q8—148no—
477#126—148no—
478#125—74no—
479#125—142no—
480#123—148no—
481C22⋊Q8—22no—
482C22⋊Q8—74no—
483C22⋊Q8—148no—
484C22⋊Q8—148no—
485C22⋊Q8—142no—
486C22⋊Q8C22×D714yes—
487#121—22no—
488#121—74no—
489#121—142no—
490#121—148no—
491#121C22×D714yes—
492C4×Q8—74no—
493C4×Q8—142no—
494C4×D4—74no—
495C4×D4—74no—
496C4×D4—74no—
497C4×D4—142no—
498C4×D4—148no—
499C4×D4—148no—
500#117—74no—
501#117—142no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—71no—
504C2×C4⋊C4—71no—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—74no—
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⋊C4—141no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4C22×D711yescharacteristic
516C2×C4⋊C4C22×D711yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—71no—
520C2×C22⋊C4—71no—
521C2×C22⋊C4—141no—
522C2×C22⋊C4—141no—
523C2×C22⋊C4—141no—
524C2×C22⋊C4—141no—
525C2×C42—71no—
526C2×C42—141no—
527C2×C42—141no—
528#107—74no—
529#107—74no—
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#103—74no—
540#103C22×D714yes—
541#102C22×D714yes—
542C22⋊C8—74no—
543C22⋊C8—74no—
544#97—74no—
545C22×C7—22no—
546C22×C7—28no—
547C22×C7—22no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—84no—
552C22×C7#54612yes—
553C22×C7C2×#13714yes—
554C22×C7C2×#13712yes—
555C22×C7#57712yes—
556C22×C7C23×D411yescharacteristic
557C2×D7—22no—
558C2×D7—22no—
559C2×D7—22no—
560C2×D7—44no—
561C4×C7—22no—
562C4×C7—42no—
563C4×C7—42no—
564C4×C7—42no—
565C4×C7#54612yes—
566C4×C7C22×#4111yescharacteristic
567C4×C7C2×H(5,𝔽2)11yescharacteristic
568Dic7—24no—
569Dic7—22no—
570Dic7—22no—
571Dic7—22no—
572Dic7—42no—
573Dic7—42no—
574Dic7—42no—
575C24—21no—
576C24—71no—
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—148no—
586C2×Q8—141no—
587C2×Q8—144no—
588C2×Q8—141no—
589C2×Q8—142no—
590C2×Q8—148no—
591C2×Q8—142no—
592C2×Q8—142no—
593C2×Q8—284no—
594C2×Q8—284no—
595C2×Q8—288no—
596C2×Q8—284no—
597C2×Q8—284no—
598C2×Q8—288no—
599C2×Q8C23×D712yes—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—44no—
605C2×D4—74no—
606C2×D4—144no—
607C2×D4—144no—
608C2×D4—562no—
609C2×D4C23×D712yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—71no—
616C22×C4—71no—
617C22×C4—71no—
618C22×C4—72no—
619C22×C4—72no—
620C22×C4—144no—
621C22×C4—144no—
622C22×C4—141no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—144no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—144no—
630C22×C4—284no—
631C22×C4—284no—
632C22×C4—562no—
633C22×C4—562no—
634C22×C4D4×D712yes—
635C22×C4D4×D711yescharacteristic
636C22×C4C23×D712yes—
637C22×C4C23×D711yescharacteristic
638SD16—44no—
639SD16—148no—
640SD16—284no—
641M16—284no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
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—74no—
655C4⋊C4—72no—
656C4⋊C4—72no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—144no—
661C4⋊C4—144no—
662C4⋊C4—144no—
663C4⋊C4—141no—
664C4⋊C4—141no—
665C4⋊C4—144no—
666C4⋊C4C23×D712yes—
667C4⋊C4C23×D712yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—74no—
671C22⋊C4—74no—
672C22⋊C4—144no—
673C22⋊C4—144no—
674C22⋊C4—144no—
675C22⋊C4—144no—
676C42—72no—
677C42—72no—
678C42—144no—
679C42—144no—
680C2×C7—24no—
681C2×C7—82no—
682C2×C7#332014yescomplemented
683C2×C7C2×#54611yescharacteristic
684C2×C7C22×#13711yescharacteristic
685C2×C7C2×#57711yescharacteristic
686D7—42no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—72no—
694C23—142no—
695C23—142no—
696C23—142no—
697C23#647814yes—
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—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—42no—
715D4—148no—
716D4—564no—
717C2×C4—22no—
718C2×C4—24no—
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—72no—
728C2×C4—72no—
729C2×C4—72no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—144no—
734C2×C4—142no—
735C2×C4—144no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—142no—
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×#332011yescharacteristic, complemented, Sylow
758C22—28no—
759C22—22no—
760C22—22no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—84no—
765C22—142no—
766C22—142no—
767C22—142no—
768C22—284no—
769C22#9030112yes—
770C22C2×#647814yes—
771C22C2×#647812yes—
772C22#9046112yes—
773C22C22×D4×D711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—142no—
779C4—144no—
780C4—142no—
781C4—142no—
782C4—282no—
783C4—282no—
784C4—282no—
785C4#9030112yes—
786C4C2×#654811yescharacteristic
787C4C2×D7×#4111yescharacteristic
788C2—24no—
789C2—82no—
790C2—282no—
791C2#1173813914yesdirect product factor
792C2C2×#9030111yescharacteristic
793C2C22×#647811yescharacteristic
794C2C2×#9046111yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#465C2
socleC23×C7C22×D4
prime radicalC2×#90309C2
hypercenterC2×#465D7
hypocenterC7C2×#3320
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#90323C2semidirect
3. C2×C7×#465C2semidirect
4. C2×#89942C2semidirect
5. C2×#89934C2semidirect
6. C22×#6390C2semidirect
7. C2×#89883C2semidirect
8. C2×#89816C2semidirect
9. C2×#89812C2semidirect
10. #11738139C2direct (N × H)
11. C2×#89629C2semidirect
12. C2×#89639C2semidirect
13. C2×#89574C2semidirect
14. C2×#89569C2semidirect
15. C2×#89552C2semidirect
16. C2×#89529C2semidirect
34. #90323C22semidirect
47. C7×#465C22semidirect
54. #89942C22semidirect
55. #89934C22semidirect
56. #89883C22semidirect
62. C2×#6390C22semidirect
65. #89816C22semidirect
66. #89812C22semidirect
71. #89639C22semidirect
72. #89629C22semidirect
73. #89574C22semidirect
74. #89569C22semidirect
75. #89552C22semidirect
76. #89529C22semidirect
194. C2×#465D7semidirect
342. #465C2×D7semidirect
682. C2×C7#3320semidirect
757. C7C2×#3320semidirect
791. C2#11738139direct (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×#903092
C2×C7×#4652
C2×#899422
C2×#899342
C22×#63902
C2×#898832
C2×#898162
C2×#898122
#117381392
C2×#896292
C2×#896392
C2×#895742
C2×#895692
C2×#895522
C2×#895292
C2×#33207